2025Activity reportProject-Team​​​‌MATHNET

5.1 Footprint of​‌ research activities

The $\mathrm{ℳ}ath$Net​​​‌ team is committed to​ minimizing the direct environmental​‌ impact of its scientific​​ operations by adhering to​​​‌ principles of digital sobriety:​

• Low-Intensity Computation: Unlike research​‌ areas dependent on heavy​​ deep-learning training or massive​​​‌ data processing, our work​ focuses on analytical derivation​‌ and fundamental mathematics. This​​ “pen-and-paper” approach inherently results​​​‌ in a minimal carbon​ footprint. Numerical simulations are​‌ optimized to run on​​ standard workstations, avoiding the​​​‌ high energy demands of​ large-scale supercomputing clusters.
• Sustainable​‌ Mobility: We prioritize virtual​​ collaboration and selective attendance​​​‌ at international conferences. For​ European meetings, sustainable transport​‌ options are favored to​​ reduce the institutional carbon​​​‌ impact related to air​ travel.

5.2 Impact of​‌ research results

The primary​​ socio-environmental contribution of our​​​‌ research lies in the​ mathematical optimization of infrastructure​‌, which serves as​​ a critical lever for​​​‌ sustainability:

• Energy and Resource​ Efficiency: Solving large-scale network​‌ problems through rigorous mathematics​​ allows for precise infrastructure​​​‌ dimensioning. By accurately defining​ stability regions and scaling​‌ laws, our models prevent​​ the over-provisioning of hardware.​​​‌ This leads to substantial​ savings in physical resources​‌ (raw materials) and operational​​ energy consumption.
• Green Connectivity:​​​‌ Our research into Reconfigurable​ Intelligent Surfaces (RIS) and​‌ stochastic geometry aims to​​ augment network capacity without​​​‌ a proportional increase in​ power density or electromagnetic​‌ exposure, promoting more efficient​​ use of the radio​​​‌ spectrum.
• Optimization of Public​ Services: The application of​‌ our theoretical frameworks to​​ urban mobility (e.g., car-sharing​​​‌ systems) and healthcare (e.g.,​ emergency department workflows) contributes​‌ to the efficient management​​ of public resources, reducing​​​‌ congestion and improving the​ quality of social services.​‌

7.1​​ Latest software developments

7.2​​​‌ New platforms

8.1 Developing Mathematical​​​‌ Frameworks

Goal: Developing mathematical‌ frameworks intended to be‌​‌ broadly applicable to real-world​​ network problems.

This section​​​‌ includes works focused on‌ fundamental theory, including stochastic‌​‌ geometry, hyperuniformity, rigidity, and​​ queuing theory. These establish​​​‌ the "tools" and "laws"‌ used to understand complex‌​‌ systems.

1. On the​​ Study of Random Measures​​​‌ Associated with Gaussian Processes‌ 20  This thesis is‌​‌ devoted to the study​​ of certain random measures​​​‌ and point processes arising‌ from Gaussian fields, with‌​‌ a focus on their​​ properties of almost-periodicity, rigidity,​​​‌ and hyperuniformity. The latter‌ two notions form the‌​‌ core of this work,​​ and we take the​​​‌ time to briefly define‌ them in this introduction.‌​‌ Hyperuniformity is a characteristic​​ common to a wide​​​‌ range of biological and‌ physical systems, ranging from‌​‌ the organisation of atoms​​ in a cell to​​​‌ the distribution of stars‌ in the cosmos. It‌​‌ originates from the principle​​ of least action, which​​​‌ states that a physical‌ system tends to prefer‌​‌ a stable equilibrium when​​ at rest. Contrary to​​​‌ what intuition might suggest,‌ these stable configurations can‌​‌ appear locally disordered, but​​ at the macroscopic scale,​​​‌ they exhibit a certain‌ regularity, a regularity that‌​‌ leads to a phenomenon​​ of hyperuniformity common to​​​‌ many physical systems. As‌ for rigidity, it is‌​‌ a purely mathematical concept,​​ and it involves asking​​​‌ whether, starting from a‌ partially observed system of‌​‌ particles, it is possible​​ to recover information about​​​‌ the unobserved part of‌ the process. By information,‌​‌ we mean the exact​​ number of hidden points,​​​‌ their centre of mass,‌ or even their exact‌​‌ distribution, . . .​​ Hyperuniformity and rigidity are​​​‌ not orthogonal concepts, and‌ it has been shown‌​‌ that many hyperuniform processes​​ exhibit a certain form​​​‌ of rigidity, at least‌ in low dimensions. This‌​‌ link between hyperuniformity and​​ rigidity is all the​​​‌ more surprising given that‌ there are very few‌​‌ systematic methods available to​​ study the rigidity of​​​‌ a particle system. In‌ this thesis, we continue‌​‌ the study of these​​ two phenomena. The first​​​‌ topic addressed in this‌ work is related to‌​‌ the nodal lines of​​ the Arithmetic Gaussian Random​​​‌ Wave. The latter are‌ known to exhibit a‌​‌ variance cancellation reminiscent of​​ hyperuniformity, as well as​​​‌ a phenomenon referred to‌ as full-correlation. We show‌​‌ that the latter is​​ linked with an almost-periodicity​​​‌ induced by the arithmetic‌ structure of the torus.‌​‌ In the subsequent chapters,​​ we move away from​​​‌ nodal sets and turn‌ to the problem of‌​‌ generating disordered samples from​​ random fields. To this​​​‌ end, we introduce a‌ new procedure that enables‌​‌ the generation of stationary​​ measures via a perturbation​​​‌ of their Palm measure.‌ The study of this‌​‌ model is pursued in​​ Chapter 5, where we​​​‌ focus on the hyperuniformity‌ properties of these perturbed‌​‌ Palm processes.

2. Asymptotic​​ fluctuations of smooth linear​​​‌ statistics of independently perturbed‌ lattices 30  We consider‌​‌ the hyperuniform model of​​​‌ d-dimensional integer lattice perturbed​ by independent random variables​‌ and we investigate the​​ large scale asymptotic fluctuations​​​‌ of smoothed versions of​ the usual counting statistics,​‌ specifically of linear statistics​​ associated to a smooth​​​‌ function with rapid decay​ at infinity. We highlight​‌ three distinct classes of​​ limit, depending on the​​​‌ dimension d and on​ the tails of the​‌ perturbations. On the one​​ hand, we establish that​​​‌ for dimensions larger than​ two, central limit theorems​‌ hold under mild assumptions​​ on the perturbations. This​​​‌ confirms numerical observations from​ physics, suggesting that even​‌ for highly correlated hyperuniform​​ models, large dimensions favor​​​‌ asymptotic normality. On the​ other hand, in dimension​‌ one, the limiting distribution​​ can be Gaussian, non-Gaussian​​​‌ with finite moments of​ all orders, or stable​‌ with parameter strictly between​​ one and two. These​​​‌ two latter results represent​ rare examples of non-Gaussian​‌ limits for smooth linear​​ statistics of hyperuniform point​​​‌ processes of Classes I​ and II.

3. Minimax​‌ estimation of the structure​​ factor of spatial point​​​‌ processes 31  We investigate​ the problem of estimating​‌ the structure factor, or​​ spectra, of stationary spatial​​​‌ point processes. In the​ first part, we establish​‌ a minimax lower bound​​ for this estimation problem,​​​‌ using an approach tailored​ to second-order properties of​‌ spatial point processes. Although​​ not the main focus,​​​‌ this methodology also extends​ naturally to a minimax​‌ lower bound for the​​ estimation of the pair​​​‌ correlation function of spatial​ point processes. In the​‌ second part, we construct​​ a multitaper estimator that​​​‌ achieves the optimal rate​ of convergence in squared​‌ risk. Under a Brillinger-mixing​​ condition, we further establish​​​‌ a chi-square-type concentration bound.​ Finally, we propose a​‌ data-driven procedure for selecting​​ the number of tapers,​​​‌ supported by an oracle​ inequality, and we demonstrate​‌ the practical effectiveness of​​ the method through numerical​​​‌ experiments.

4. Decision-Epochs Matter:​ Unveiling Its Impact on​‌ the Stability of Scheduling​​ With Randomly Varying Connectivity​​​‌ 9  A classical result​ in queuing theory states​‌ that in a parallel-queue​​ single-server model, the maximum​​​‌ stability region is unaffected​ by scheduling decision epochs,​‌ and in particular is​​ the same for preemptive​​​‌ and non-preemptive systems. We​ examine a scenario where​‌ queues are randomly connected​​ to the server and​​​‌ show that, unlike the​ classical case, the maximum​‌ stability region strongly depends​​ on the scheduling decision​​​‌ epochs. We compare three​ settings: decisions can be​‌ made anytime (unconstrained), decisions​​ are made only at​​​‌ departures (non-preemptive), and decisions​ occur when a $\mathrm{\gamma ‌}$-rate exponential clock rings.​​ We observe a significant​​​‌ reduction in the stability​ region in the non-preemptive​‌ setting compared to the​​ unconstrained one, showing that​​​‌ a non-preemptive scheduler cannot​ take opportunistically advantage of​‌ the random varying connectivity.​​ Also, in the $\mathrm{\gamma ‌}$-rate clock setting, one​ can be arbitrarily close​‌ to the maximum stability​​ region in the unconstrained​​​‌ setting if we choose​ γ large enough. In​‌ all the settings, we​​ show that the Longest​​​‌ Connected Queue (LCQ) policy​ achieves maximum stability. From​‌ a methodological viewpoint, we​​ introduce a new theoretical​​ tool called "test for​​​‌ fluid limits" (TFL), which‌ offers a method to‌​‌ determine stability on the​​ basis of a simple​​​‌ formal test.

5. Online‌ matching for the multiclass‌​‌ stochastic block model 10​​  We consider the problem​​​‌ of sequential matching in‌ a stochastic block model‌​‌ with several classes of​​ nodes and generic compatibility​​​‌ constraints. When the probabilities‌ of connections do not‌​‌ scale with the size​​ of the graph, we​​​‌ show that under the‌ NCOND condition, a simple‌​‌ max-weight type policy allows​​ to attain an asymptotically​​​‌ perfect matching while no‌ sequential algorithm attain perfect‌​‌ matching otherwise. The proof​​ relies on a specific​​​‌ Markovian representation of the‌ dynamics associated with Lyapunov‌​‌ techniques.

6. Functional central​​ limit theorem for topological​​​‌ functionals of Gaussian critical‌ points 24  We consider‌​‌ Betti numbers of the​​ excursion of a smooth​​​‌ Euclidean Gaussian field restricted‌ to a rectangular window,‌​‌ in the asymptotics where​​ the window grows to​​​‌ ${ℝ}^d$ . With‌ motivations coming from Topological‌​‌ Data Analysis, we derive​​ a functional Central Limit​​​‌ Theorem where the varying‌ argument is the thresholding‌​‌ parameter, under assumptions of​​ regularity and covariance decay​​​‌ for the field and‌ its derivatives. We also‌​‌ show fixed-level CLTs coming​​ from martingale based techniques​​​‌ inspired from the theory‌ of geometric stabilisation, and‌​‌ limiting non-degenerate variance.

7.​​ Higher-order Monte Carlo cluster​​​‌ dynamics for community detection‌ in Euclidean graphs 16‌​‌  We study GIBBS distributions​​ with competing interactions and​​​‌ propose a higher-order extension‌ of the SWENDSEN–WANG dynamics‌​‌ that incorporates triangular bonds.​​ The new dynamics preserves​​​‌ the same stationary distribution,‌ alleviates frustration, and yields‌​‌ markedly better sampling. When​​ applied to a synthetic​​​‌ Euclidean-graph community-detection benchmark, our‌ algorithm outperforms existing methods.‌​‌

8. Poisson approximation of​​ fixed-degree nodes in weighted​​​‌ random connection models 23‌  We present a process-level‌​‌ Poisson-approximation result for the​​ degree-$k$ vertices in​​​‌ a highdensity weighted random‌ connection model with preferential-attachment‌​‌ kernel in the unit​​ volume. Our main focus​​​‌ lies on the impact‌ of the left tails‌​‌ of the weight distribution​​ for which we establish​​​‌ general criteria based on‌ their small-weight quantiles. To‌​‌ illustrate that our conditions​​ are broadly applicable, we​​​‌ verify them for weight‌ distributions with polynomial and‌​‌ stretched exponential left tails.​​ The proofs rest on​​​‌ truncation arguments and a‌ recently established quantitative Poisson‌​‌ approximation result for functionals​​ of Poisson point processes.​​​‌

9. Hyperuniform random measures,‌ transport and rigidity 26‌​‌  This survey explores the​​ foundational theory and recent​​​‌ developments in the study‌ of hyperuniformity. We present‌​‌ a comprehensive mathematical framework​​ in the context of​​​‌ weakly stationary random measures,‌ emphasizing spectral characterizations and‌​‌ second order asymptotics. Classical​​ examples - including determinantal​​​‌ point processes, Gibbs measures,‌ and zero sets of‌​‌ Gaussian analytic functions -​​ are presented in depth​​​‌ to illustrate core principles.‌ We also highlight recent‌​‌ progress connecting hyperuniformity with​​ optimal transport and rigidity​​​‌ phenomena, pointing to emerging‌ directions in the field.‌​‌

10. Maximal rigidity of​​ random measure and uniqueness​​​‌ pairs: stealthy processes, quasicrystals‌ and periodicity 27  This‌​‌ article investigates the phenomenon​​​‌ of maximal rigidity in​ spatial processes, where perfect​‌ interpolation of the process​​ is possible from partial​​​‌ information, specifically, from its​ restriction to a strict​‌ subdomain, often resulting in​​ a trivial tail algebra.​​​‌ A classical example known​ since the 1930's is​‌ that a time series​​ is fully determined by​​​‌ its values on the​ negative integers if its​‌ spectrum has a gap,​​ or at least a​​​‌ sufficiently deep zero. We​ extend such results to​‌ higher dimensions and continuous​​ settings by establishing a​​​‌ connection with the concept​ of uniqueness pairs, rooted​‌ in the uncertainty principle​​ of harmonic analysis. We​​​‌ present several other manifestations​ of this principle, unify​‌ and strengthen seemingly unrelated​​ results across different models:​​​‌ quasicrystals and stealthy processes​ are shown to be​‌ maximally rigid on cones,​​ and discrete integer-valued processes​​​‌ are necessarily periodic when​ they have a simply​‌ connected spectrum. Finally, we​​ identify a surprising class​​​‌ of continuous fields with​ seemingly standard behavior, such​‌ as linear variance and​​ finite dependency range, that​​​‌ undergo a phase transition:​ they are perfectly interpolable​‌ on $B(\mathrm{0},\rho )$ for​​​‌ $0<\rho ⩽\frac{2}{\pi }$ but exhibit​‌ no rigidity for $\mathrm{\rho }>2$.

11.​​​‌ Mean field analysis of​ stochastic networks with reservation​‌ 6  The problem of​​ reservation in a large​​​‌ distributed system is analysed​ via a new mathematical​‌ model. The target application​​ is car-sharing systems. This​​​‌ model is precisely motivated​ by the large station-based​‌ car-sharing system in France,​​ called Autolib'. This system​​​‌ can be described as​ a closed stochastic network​‌ where the nodes are​​ the stations and the​​​‌ customers are the cars.​ The user can reserve​‌ the car and the​​ parking space. In the​​​‌ paper, we study the​ evolution of the system​‌ when the reservation of​​ parking spaces and cars​​​‌ is effective for all​ users. The asymptotic behaviour​‌ of the underlying stochastic​​ network is given when​​​‌ the number $N$ of​ stations and the fleet​‌ size $M$ increase at​​ the same rate. The​​​‌ analysis involves a Markov​ process on a state​‌ space with dimension of​​ order $N^2$.​​​‌ It is quite remarkable​ that the state process​‌ describing the evolution of​​ the stations, whose dimension​​​‌ is of order $\mathrm{N}$, converges in distribution,​‌ although not Markov, to​​ an non-homogeneous Markov process.​​​‌ We prove this mean-field​ convergence. We also prove,​‌ using combinatorial arguments, that​​ the mean-field limit has​​​‌ a unique equilibrium measure​ when the time between​‌ reserving and picking up​​ the car is sufficiently​​​‌ small. This result extends​ the case where only​‌ the parking space can​​ be reserved.

12. On​​​‌ the geometry of the​ stability regions of randomly​‌ modulated queuing systems 18​​  We study the maximum​​​‌ stability region (MSR) of​ a scheduling problem involving​‌ multiple queues, a single​​ server, and randomly modulated​​​‌ dynamics. In the case​ where the modulation process​‌ is autonomous, takes values​​ in a finite set,​​​‌ and is in stationary​ regime, we characterise the​‌ stability region as a​​ Minkowski sum of deGua​​ simplices, structures known as​​​‌ cephoids in the convex‌ geometry literature. Beyond endowing‌​‌ the stability region with​​ a rich mathematical structure,​​​‌ this apparently novel connection‌ enables an explicit description‌​‌ of the MSR in​​ the 2-queue case, and​​​‌ provides a simple iterative‌ scheme to obtain its‌​‌ minimal H-description in the​​ general case.

13. Rigidity​​​‌ of random stationary measures‌ and applications to point‌​‌ processes 28  The number​​ rigidity of a point​​​‌ process $P$ entails that‌ for a bounded set‌​‌ $A$ the knowledge of​​ $P$ on $A^{\mathrm{c‌}}$ a.s. determines $P(‌A)$; the‌​‌ $k$-order rigidity means​​ we can recover the​​​‌ moments of $P{\mathrm{1‌}}_A$ up to order‌​‌ $k$. We show​​ that there is $\mathrm{k‌}$-rigidity if the continuous‌ component $s$ of $\mathrm{P‌‌}$'s structure factor has​​ a zero of order​​​‌ $k$ in 0, by‌ exploiting a connection with‌​‌ Schwartz’ Paley-Wiener theorem for​​ analytic functions of exponential​​​‌ type; these results apply‌ to any random ${\mathrm{L‌‌}}^2$ wide sense stationary​​ measure on ${ℝ}^{\mathrm{d‌}}$ or ${\mathbb{Z}}^d$.‌ In the continuous setting,‌​‌ these local conditions are​​ also necessary if $\mathrm{s‌}$ has finitely many zeros,‌ or is isotropic, or‌​‌ at the opposite separable.​​ This explains why no​​​‌ model seems to exhibit‌ rigidity in dimension $\mathrm{d‌‌}\ge 3$, and​​ allows to efficiently recover​​​‌ many recent rigidity results‌ about point processes. In‌​‌ the discrete setting, these​​ results hold provided $\#‌A>2\mathrm{k‌}$. We derive new‌​‌ results about models of​​ cluster lattices and give​​​‌ the first example of‌ a stationary point process‌​‌ $P\subset {ℝ}^{\mathrm{d}}$ exhibiting arbitrary low decay​​​‌ of the structure factor‌ in 0, hence arbitrary‌​‌ high order of rigidity.​​ For a continuous Determinantal​​​‌ point process with kernel‌ $\kappa$, $k$-rigidity‌​‌ is equivalent to ${(1-\widehat{{\kappa }^{\mathrm{2‌}}})}^{-\mathrm{1‌}}$ having a zero of‌​‌ order $2k$ in​​ 0, which answers questions​​​‌ on completeness and number‌ rigidity. We also explore‌​‌ the consequences of these​​ statements in the less​​​‌ tractable realm of Riesz‌ gases.

14. Stochastic domination‌​‌ and lifts of random​​ variables in percolation theory​​​‌ 29  Consider some matrix‌ waiting for its coefficients‌​‌ to be written. For​​ each column, sample independently​​​‌ one Bernoulli random variable‌ of some parameter $\mathrm{p‌‌}$. Seeing all this​​ and possibly using extra​​​‌ randomness, Alice then chooses‌ one spot in each‌​‌ column, in any way​​ she wants. When the​​​‌ Bernoulli random variable of‌ some column is equal‌​‌ to 1, the number​​ 1 is written in​​​‌ the chosen spot. When‌ the Bernoulli random variable‌​‌ of a column is​​ 0, nothing is done​​​‌ on this column. We‌ prove that, using extra‌​‌ randomness, it is possible​​ for Bob to fill​​​‌ the empty spots with‌ well chosen 0's and‌​‌ 1's so that the​​ entries of the matrix​​​‌ are independent Bernoulli random‌ variables of parameter $\mathrm{p‌‌}$. We investigate various​​ generalisations and variations of​​​‌ this problem, and use‌ this result to revisit‌​‌ and generalise (nonstrict) monotonicity​​​‌ of the percolation threshold​ $p_c$ with respect​‌ to some sort of​​ graph-quotienting, namely fibrations. In​​​‌ a second part, which​ is independent of the​‌ first one, we revisit​​ strict monotonicity of ${\mathrm{p‌}}_c$ with respect to​ fibrations, a result that​‌ naturally requires more assumptions​​ than its nonstrict counterpart.​​​‌ We reprove the bond-percolation​ case of the result​‌ of Martineau and Severo​​ without resorting to essential​​​‌ enhancements, using couplings instead.​

15. On a class​‌ of dynamical Poisson-Voronoi tessellations​​ 21  Consider a dynamical​​​‌ network model featuring mobile​ stations on the Euclidean​‌ plane. The initial locations​​ of the stations are​​​‌ given by a homogeneous​ Poisson point process. The​‌ stations are all moving​​ at a constant speed​​​‌ and in a random​ direction. Consider fixed users​‌ located in the Euclidean​​ plane, which are served​​​‌ by the mobile stations.​ Each user stays connected​‌ to the nearest station​​ at any given point​​​‌ of time. Since the​ stations are moving, an​‌ user disconnects and connects​​ with different stations over​​​‌ time, by always selecting​ which ever station is​‌ the closest. This gives​​ rise to a dynamical​​​‌ version of the Poisson-Voronoi​ tessellation. The focus of​‌ this paper is on​​ the sequence of "handover"​​​‌ events of a typical​ user, which are the​‌ epochs when its association​​ changes. This defines a​​​‌ point process on the​ time-axis, the "handover point​‌ process". We show that​​ this point process is​​​‌ stationary and we determine​ its main properties, in​‌ particular its intensity and​​ the joint distribution of​​​‌ its inter-event times. We​ also analyze the handover​‌ Palm distributions of several​​ variables of practical interest.​​​‌ This includes the distance​ to the closest mobile​‌ stations and the point​​ process of all other​​​‌ mobile stations at handover​ epochs. The analysis is​‌ conducted both in the​​ single-speed and in the​​​‌ multi-speed scenarios. It leads​ to the identification of​‌ the three dimensional state​​ variables that "Markovize" the​​​‌ association dynamics. The analysis​ is based on a​‌ specific system of non-compact​​ particles. The motivations are​​​‌ in the modeling of​ low or medium orbit​‌ satellite wireless communication networks.​​ The model studied here​​​‌ is a planar "caricature"​ of this problem, which​‌ is initially defined on​​ the sphere.

8.2 Exploring​​​‌ and Validating Practical Applications​

Goal: Exploring and validating​‌ the practical applications of​​ the aforementioned frameworks.

This​​​‌ section covers applications of​ the aforementioned theories to​‌ specific domains, including 5G/6G​​ wireless networks—specifically those utilizing​​​‌ reconfigurable intelligent surfaces (RIS)​ and non-terrestrial networks (NTN)—as​‌ well as car-sharing systems​​ (Autolib'), emergency department workflows,​​​‌ and biological neural networks.​

16. On multiclass spatial​‌ birth-and-death processes with wireless-type​​ interactions 8  This paper​​​‌ studies a multiclass spatial​ birth-and-death (SBD) processes ona​‌ compact region of the​​ Euclidean plane modeling wireless​​​‌ interactions. In thismodel, users​ arrive at a constant​‌ rate and leave at​​ a rate function of​​​‌ the inter-ference created by​ other users in the​‌ network. The novelty of​​ this work lies inthe​​​‌ addition of service differentiation,​ inspired by bandwidth partitioning​‌ presentin 5G networks: users​​ are allocated a fixed​​ number of frequency bands​​​‌ and onlyinterfere with transmissions‌ on these bands.The first‌​‌ result of the paper​​ is the determination of​​​‌ the critical user arrival‌ ratebelow which the system‌​‌ is stochastically stable, and​​ above which it is​​​‌ unstable.The analysis requires symmetry‌ assumptions which are defined‌​‌ in the paper. Theproof​​ for this result uses​​​‌ stochastic monotonicity and fluid‌ limit models. Themonotonicity allows‌​‌ one to bound the​​ dynamics from above and​​​‌ below by twoadequate discrete-state‌ Markov jump processes, for‌​‌ which we obtain stability​​ andinstability results using fluid​​​‌ limits. This leads to‌ a closed form expression‌​‌ for thecritical arrival rate.​​ The second contribution consists​​​‌ in two heuristics to‌ estimatethe steady-state densities of‌​‌ all classes of users​​ in the network: the​​​‌ first one relieson a‌ Poisson approximation of the‌​‌ steady-state processes. The second​​ one uses acavity approximation​​​‌ leveraging second-order moment measures,‌ which leads tomore accurate‌​‌ estimates of the steady-state​​ user densities. The Poisson​​​‌ heuristicalso gives a good‌ estimate for the critical‌​‌ arrival rate.

17. Performance​​ Guarantees of Cellular Networks​​​‌ with Hardcore Regulation and‌ Scheduling 14  Providing performance‌​‌ guarantees is one of​​ the critical objectives of​​​‌ recent and future communication‌ networks, toward which regulations,‌​‌ i.e., constraints on key​​ system parameters, have played​​​‌ an indispensable role. This‌ is the case for‌​‌ large wireless communication networks,​​ where spatial regulations (e.g.,​​​‌ constraints on intercell distance)‌ have recently been shown,‌​‌ through a spatial network​​ calculus, to be essential​​​‌ for establishing provable wireless‌ link-level guarantees. In this‌​‌ work, we focus on​​ performance guarantees for the​​​‌ downlink of cellular networks‌ where we impose a‌​‌ hardcore (spatial) regulation on​​ base station (BS) locations​​​‌ and evaluate how BS‌ scheduling (which controls which‌​‌ BSs can transmit at​​ a given time) impacts​​​‌ performance. Hardcore regulation is‌ the simplest form of‌​‌ spatial regulation that enforces​​ a minimal distance between​​​‌ any pair of transmitters‌ in the network. Within‌​‌ this framework of spatial​​ network calculus, we first​​​‌ provide an upper bound‌ on the power of‌​‌ total interference for a​​ spatially regulated cellular network,​​​‌ and then, identify the‌ regimes where scheduling BSs‌​‌ yields better link-level rate​​ guarantees compared to scenarios​​​‌ where base stations are‌ always active. The hexagonal‌​‌ cellular network is analyzed​​ as a special case.​​​‌ The results offer insights‌ into what spatial regulations‌​‌ are needed, when to​​ choose scheduling, and how​​​‌ to potentially reduce the‌ network power consumption to‌​‌ provide a certain target​​ performance guarantee.

18. Statistical​​​‌ Learning of Traffic Load‌ from Demand in Wireless‌​‌ Cellular Networks: A Cell-by-Cell​​ Approach 13  A statistical​​​‌ approach is proposed to‌ predict the specific load‌​‌ of each cell in​​ operational wireless networks, using​​​‌ traffic demand as the‌ main variable. Unlike a‌​‌ global linear model, which​​ is fitted using data​​​‌ from all cells uniformly‌ without considering the specific‌​‌ characteristics of each cell,​​ the cellwise linear approach​​​‌ is distinguished by two‌ key elements: (i) a‌​‌ unidimensional model, in which​​ the load of each​​​‌ cell is predicted solely‌ based on its own‌​‌ traffic demand, and (ii)​​​‌ a multidimensional model, in​ which the traffic demand​‌ of all the cells​​ is incorporated. Using large-scale​​​‌ real-world data, it is​ shown that the unidimensional​‌ model outperforms global approaches​​ in terms of accuracy.​​​‌ While additional flexibility and​ improvements are offered by​‌ the multidimensional model in​​ specific scenarios, particularly under​​​‌ high traffic conditions, its​ coefficients often seem to​‌ lack physical interpretability, even​​ when using ridge regularization.​​​‌ This underscores the need​ for more advanced regularization​‌ techniques to be developed​​ and particularly, ones that​​​‌ account for the geometry​ of wireless networks.

19.​‌ Localized Statistical Learning of​​ Cell Loads in Cellular​​​‌ Networks 12  Accurate cell​ load prediction is crucial​‌ for efficient wireless networks.​​ This paper investigates localized​​​‌ statistical learning, using a​ varying number of input​‌ neighboring cells k to​​ optimize load estimation. Using​​​‌ real-world operational data, different​ prediction methods are benchmarked,​‌ such as neural networks​​ (NNs), linear fitting and​​​‌ ridge regularization. Experiments compellingly​ show that NNs incorporating​‌ activation functions achieve superior​​ prediction performance. An optimal​​​‌ range for k is​ identified to be around​‌ 20-30 neighbors, demonstrating an​​ essential balance between model​​​‌ complexity and generalization. Notably,​ the study affirms the​‌ robustness of this approach​​ against stochastic training variations​​​‌ and highlights the benefits​ of sufficient training data.​‌ Thus, this work underscores​​ the efficacy of localized,​​​‌ non-linear models, offering robust​ insights and paving the​‌ way for deep learning​​ approaches to cell load​​​‌ prediction.

20. Statistical Learning​ for Quality of Service​‌ Evaluation and Dimensioning of​​ Wireless Networks 19  Accurate​​​‌ prediction of the cellular​ network load relative to​‌ a traffic demand is​​ essential for strategic network​​​‌ planning and resource management.​ This thesis evaluates a​‌ range of predictive models,​​ from physics-based mathematical frameworks​​​‌ to data-driven statistical learning​ methods, to identify the​‌ most robust and efficient​​ approaches for this task.For​​​‌ short-term forecasting, the investigation​ reveals that cell specific,​‌ complex non-linear models achieve​​ the highest accuracy. Specifically,​​​‌ a neural network that​ considers traffic from a​‌ localized neighborhood of nearby​​ cells outperforms global benchmarks.​​​‌ This demonstrates the importance​ of capturing local spatial​‌ dependencies, while carefully managing​​ model complexity to avoid​​​‌ the overfitting, that occurs​ when using data from​‌ the entire network.Another major​​ contribution of this work​​​‌ is the analysis of​ long-term performance in the​‌ presence of temporal drift,​​ namely the natural evolution​​​‌ of network dynamics over​ time. On horizons extending​‌ up to two years,​​ a striking reversal in​​​‌ performance is observed. The​ complex models, so effective​‌ in the short term,​​ suffer significant accuracy degradation.​​​‌ In their place, physics-based​ and simpler models demonstrate​‌ remarkable resilience. Indeed, a​​ basic data-driven model that​​​‌ uses only a cell’s​ own historical traffic consistently​‌ delivers the most reliable​​ long-term forecasts, rivaled only​​​‌ by the aforementioned mathematical​ model.This thesis concludes that​‌ a fundamental trade-off exists​​ between short-term accuracy and​​​‌ long-term stability. For the​ strategic, long-horizon applications required​‌ by network operators, model​​ simplicity and resistance to​​​‌ overfitting thus prove to​ be more critical factors​‌ for success than the​​ capacity to model intricate,​​ transient spatial patterns.

21.​​​‌ Data Science: From Statistics‌ to Machine Learning and‌​‌ Deep Learning, with Applications​​ to Wireless Networks 25​​​‌  This book offers a‌ rigorous, self-contained introduction to‌​‌ the mathematical foundations of​​ machine learning, from its​​​‌ roots in multivariate statistics‌ to modern deep learning‌​‌ architectures. A defining feature​​ of this work is​​​‌ its commitment to mathematical‌ rigor; unlike approaches that‌​‌ treat algorithms as "black​​ boxes," key concepts are​​​‌ introduced through precise definitions‌ and established via theorems‌​‌ with complete proofs. This​​ principled approach is particularly​​​‌ evident in the formal‌ treatment of measurability issues,‌​‌ a topic often glossed​​ over in the learning​​​‌ theory literature.The book is‌ organized into three parts.‌​‌ The first two parts​​ cover the theoretical core​​​‌ of multivariate statistics and‌ machine learning, including linear‌​‌ models, logistic regression, learnability​​ (VC theory), and neural​​​‌ networks.The third part bridges‌ the gap between theory‌​‌ and practice with an​​ in-depth case study on​​​‌ predicting Quality of Service‌ (QoS) in large-scale wireless‌​‌ networks. Using operational data​​ from a major European​​​‌ operator, we demonstrate how‌ the theoretical frameworks are‌​‌ implemented and validated in​​ a real-world engineering context.​​​‌ By combining a rigorous‌ theoretical exposition with a‌​‌ significant practical application, this​​ book aims to provide​​​‌ a complete and actionable‌ guide for both researchers‌​‌ and practitioners in data​​ science.

22. Large-scale analysis​​​‌ of load-balancing policies for‌ free-floating car-sharing models 15‌​‌  In free-floating (FF) car-sharing​​ systems, FF cars share​​​‌ parking spaces in public‌ space with much more‌​‌ numerous private cars. The​​ system is modeled as​​​‌ a closed queueing network‌ with two classes of‌​‌ customers, FF and private​​ cars, with different orders​​​‌ of magnitude. They move‌ between N nodes, each‌​‌ with a large capacity​​ CN , C positive.​​​‌ Mean-field techniques are adapted‌ to the presence of‌​‌ private cars, which act​​ as a fast-varying random​​​‌ environment. This allows us‌ to study the impact‌​‌ of load-balancing policies on​​ the distribution of the​​​‌ number of FF cars‌ per zone when the‌​‌ system gets large. For​​ two load-balancing policies, respectively​​​‌ modifying the routing probabilities‌ and the pick-up rates,‌​‌ we obtain an explicit​​ distribution, a binomial negative​​​‌ distribution driven by a‌ fixed point equation. The‌​‌ influence of parameters on​​ performance is derived.

23.​​​‌ Thermodynamical limits for models‌ of car-sharing systems: the‌​‌ Autolib' example 5  We​​ analyze mean-field equations obtained​​​‌ for models motivated by‌ a large station-based car-sharing‌​‌ system in France called​​ Autolib’. The main focus​​​‌ is on a version‌ where users reserve a‌​‌ parking space when they​​ take a car. In​​​‌ a first model, the‌ reservation of parking spaces‌​‌ is effective for all​​ users and capacity constraints​​​‌ are ignored. The model‌ is carried out in‌​‌ the thermodynamical limit, that​​ is when the number​​​‌ $N$ of stations and‌ the number of cars‌​‌ $M_N$ tend to​​ infinity, with $U=‌{lim}_{N\to \mathrm{\infty ‌}}{M}_N/\mathrm{N‌‌}$. This limit is​​ described by Kolmogorov’s equations​​​‌ of a two-dimensional time-inhomogeneous‌ Markov process depicting the‌​‌ numbers of reservations and​​​‌ cars at a station.​ It satisfies a non-linear​‌ differential system. We prove​​ analytically that this system​​​‌ has a unique solution,​ which converges, as $\mathrm{t‌}\to \infty$, to​​ an equilibrium point exponentially​​​‌ fast. Moreover, this equilibrium​ point corresponds to the​‌ stationary distribution of a​​ two-queue tandem (reservations, cars),​​​‌ which is here always​ ergodic. The intensity factor​‌ of each queue has​​ an explicit form obtained​​​‌ from an intrinsic mass​ conservation relationship. Two related​‌ models with capacity constraints​​ are briefly presented: the​​​‌ simplest one with no​ reservation leads to a​‌ one-dimensional problem; the second​​ one corresponds to our​​​‌ first model with finite​ total capacity $K$.​‌

24. Stability and renormalization​​ of Jackson networks with​​​‌ non-idling mobile servers 22​  A tandem of two​‌ queues sharing a pool​​ of servers, where users​​​‌ take the time to​ switch to thesecond queue,​‌ is used to model​​ a typical pathway through​​​‌ an emergency department (ED),​ wherepatients undergo two consultations​‌ separated by diagnostic tests.​​ In this article, explicit​​​‌ conditionsfor ergodicity and transience​ are given and proven​‌ via Foster’s criterion, using​​ a linear Lyapunovfunction. This​​​‌ result is extended to​ a Jackson network, with​‌ the key difference that​​ the nodes sharea pool​​​‌ of servers, with a​ non-idling service policy. Further,​‌ the delay times for​​ customers to movefrom one​​​‌ node to another must​ be taken into account.​‌ This covers some of​​ the main features ofmodels​​​‌ for emergency departments, namely​ priorities (triage) between patients.​‌ In the case of​​ thetandem queue, by scaling​​​‌ the arrival rate and​ the number of servers​‌ by N, we obtain​​ a renormalizedprocess converging to​​​‌ the solution of an​ ordinary differential equation (ODE)​‌ subject to boundaryconditions. When​​ the system is ergodic,​​​‌ we discuss the solution​ of this ODE as​‌ $t\to \infty$.​​

25. Analysis of a​​​‌ Spatially Correlated Vehicular Network​ Assisted by Cox-Distributed Vehicle​‌ Relays 4  In vehicle-to-everything​​ (V2X) communications, roadside units​​​‌ (RSUs) play an essential​ role in connecting various​‌ network devices. In some​​ cases, users may not​​​‌ be well-served by RSUs​ due to congestion, attenuation,​‌ or interference. In these​​ cases, vehicular relays associated​​​‌ with RSUs can be​ used to serve those​‌ users. This paper uses​​ stochastic geometry to model​​​‌ and analyze a spatially​ correlated heterogeneous vehicular network​‌ where both RSUs and​​ vehicular relays serve network​​​‌ users such as pedestrians​ or other vehicles. We​‌ present an analytical model​​ where the spatial correlation​​​‌ between roads, RSUs, relays,​ and users is systematically​‌ modeled via Cox point​​ processes. Assuming users are​​​‌ associated with either RSUs​ or relays, we derive​‌ the association probability and​​ the coverage probability of​​​‌ the typical user. Then,​ we derive the user​‌ throughput by considering interactions​​ of links unique to​​​‌ the proposed network. This​ paper gives practical insights​‌ into designing spatially correlated​​ vehicular networks assisted by​​​‌ vehicle relays. For instance,​ we express network performance​‌ such as user association,​​ signal-to-interference (SIR) coverage probability,​​​‌ and network throughput as​ the functions of network​‌ key geometric parameters. In​​ practice, this helps one​​ to optimize the network​​​‌ so as to achieve‌ ultra reliability or maximum‌​‌ user throughput of the​​ vehicular networks by varying​​​‌ key aspects such as‌ the relay density or‌​‌ the bandwidth for relays.​​

26. A Stochastic Geometry​​​‌ Framework for Performance Analysis‌ of RIS-assisted OFDM Cellular‌​‌ Networks 11  The reconfigurable​​ intelligent surface (RIS) technology​​​‌ allows one to engineer‌ spatial diversity in complex‌​‌ cellular networks. This paper​​ provides a stochastic geometry​​​‌ framework for the system-level‌ performance assessment of RIS-assisted‌​‌ networks. To account for​​ the inherent randomness in​​​‌ the spatial deployments of‌ base stations (BSs) and‌​‌ RISs, we model the​​ RIS placements as point​​​‌ processes (PPs) conditioned on‌ the associated BSs, which‌​‌ are modeled by a​​ Poisson point process (PPP).​​​‌ We assume that the‌ system uses the orthogonal‌​‌ frequency division multiplexing (OFDM)​​ technique to exploit the​​​‌ multipath diversity provided by‌ RISs. The downlink coverage‌​‌ probability and ergodic rate​​ can be evaluated when​​​‌ RISs operate as batched‌ powerless beamformers. The resulting‌​‌ analytical expressions provide a​​ general methodology for assessing​​​‌ the impact of a‌ parameterized RIS model on‌​‌ system performance. These RIS​​ PPs can be adapted​​​‌ based on the deployment‌ strategy. We focus on‌​‌ modeling the RISs as​​ a Matérn cluster process​​​‌ (MCP), where each RIS‌ cluster is a finite‌​‌ PPP within a ring​​ centered on its associated​​​‌ BS. This model connects‌ link-level knowledge to system-level‌​‌ impacts, such as overall​​ interference and the effects​​​‌ of imperfect channel state‌ information (CSI). It also‌​‌ evaluates key RIS deployment​​ parameters, including batch size​​​‌ and RIS density. Furthermore,‌ we analyze a variant‌​‌ of RIS placement in​​ which RISs are deployed​​​‌ around coverage holes to‌ demonstrate the framework’s flexibility‌​‌ and applicability. Numerical evaluations​​ of the analytical expressions​​​‌ and Monte-Carlo simulations jointly‌ validate the proposed analytical‌​‌ approach and provide valuable​​ insights into the design​​​‌ of future RIS-assisted cellular‌ networks.

27. How Much‌​‌ Can Reconfigurable Intelligent Surfaces​​ Augment Sky Visibility: A​​​‌ Stochastic Geometry Approach 7‌  This paper uses the‌​‌ theory of point processes​​ and stochastic geometry to​​​‌ quantify the sky visibility‌ experienced by users located‌​‌ in an outdoor environment.​​ The general idea is​​​‌ to represent the buildings‌ of this environment as‌​‌ a stationary marked point​​ process, where the points​​​‌ represent the building locations‌ and the marks their‌​‌ heights. The point process​​ framework is first used​​​‌ to characterize the distribution‌ of the blockage angle,‌​‌ which limits the visibility​​ of a typical user​​​‌ into the sky dueto‌ the obstruction by buildings.‌​‌ In the context of​​ communications,this distribution is useful​​​‌ when users try to‌ connect to the nodes‌​‌ of an aerial or​​ non-terrestrial network in a​​​‌ Line-of-Sight way. Within this‌ context, the point process‌​‌ framework can also be​​ used to investigate the​​​‌ gain of connectivity obtained‌ thanks to Reconfigurable Intelligent‌​‌ Surfaces. Assuming that such​​ surfaces are installed on​​​‌ the top of buildings‌ to extend the user’s‌​‌ sky visibility, this point​​ process approach allows one​​​‌ to quantify the gain‌ in visibility and hence‌​‌ the gain in connectivity​​​‌ obtained by the typical​ user. The distributional properties​‌ of visibility-relatedmetrics are cross-validated​​ by comparison to simulation​​​‌ results and 3GPP measurements​

28. A Novel Analytical​‌ Model for LEO and​​ MEO Satellite Networks based​​​‌ on Cox Point Processes​ 2  This work develops​‌ an analytical framework for​​ downlink low Earth orbit​​​‌ (LEO) or medium Earth​ orbit (MEO) satellite communications,​‌ leveraging tools from stochastic​​ geometry. We propose a​​​‌ tractable approach to the​ analysis of such satellite​‌ communication systems, accounting for​​ the fact that satellites​​​‌ are located on circular​ orbits. We accurately incorporate​‌ this geometric property of​​ LEO or MEO satellite​​​‌ constellations by developing a​ Cox point process model​‌ that jointly produces orbits​​ and satellites on these​​​‌ orbits. Our work contrasts​ with previous modeling studies​‌ that presumed satellite locations​​ to be entirely random,​​​‌ thereby overlooking the fundamental​ fact that satellites are​‌ jointly positioned on orbits.​​ Employing this Cox model,​​​‌ we analyze the network​ performance experienced by users​‌ located on Earth. Specifically,​​ we evaluate the no-satellite​​​‌ probability of the proposed​ network and the Laplace​‌ transform of the interference​​ created by such a​​​‌ network. Using it, we​ compute its SIR (signalto-interference)​‌ distribution, namely its coverage​​ probability. By presenting fundamental​​​‌ network performance as functions​ of key parameters, this​‌ model allows one to​​ assess the statistical properties​​​‌ of downlink LEO or​ MEO satellite communications and​‌ can thus be used​​ as a system-level design​​​‌ tool to operate and​ optimize forthcoming complex LEO​‌ or MEO satellite networks.​​

29. Stochastic Geometry and​​​‌ Dynamical System Analysis of​ Walker Satellite Constellations 3​‌  In practice, low Earth​​ orbit (LEO) and medium​​​‌ Earth orbit (MEO) satellite​ networks consist of multiple​‌ orbits which are populated​​ with many satellites. A​​​‌ widely used spatial architecture​ for LEO or MEO​‌ satellites is the Walker​​ constellation, where the longitudes​​​‌ of orbits are evenly​ spaced and the satellites​‌ are equally spaced along​​ the orbits. In this​​​‌ paper, we develop a​ stochastic geometry model for​‌ the Walker constellations. This​​ proposed model enables an​​​‌ analysis based on dynamical​ system theory, which allows​‌ one to address essential​​ structural properties such as​​​‌ periodicity and ergodicity. It​ also enables a stochastic​‌ geometry analysis under which​​ we derive the performance​​​‌ of downlink communications of​ a typical user at​‌ a given latitude, as​​ a function of the​​​‌ key constellation parameters.

30.​ Spectrum Coexistence Between Passive​‌ Satellites and Terrestrial Network​​ via Chernoff Bounds 17​​​‌  We develop tractable characterizations​ of the interference resulting​‌ from terrestrial cellular networks​​ radiating towards passive satellite​​​‌ sensing receivers. Such a​ setting has important implications​‌ for the future allocation​​ and terrestrial use of​​​‌ spectrum in the 100​ to 300 GHz band.​‌ Building on a recently​​ developed stochastic geometry approach,​​​‌ we focus on the​ outage probability experienced by​‌ to a constellation of​​ satellite sensors, which depends​​​‌ upon the distribution of​ the interference experienced by​‌ a typical satellite sensor.​​ The distribution is a​​​‌ function of spatial and​ temporal randomness. We obtain​‌ upper bounds on the​​ outage probability using a​​ large deviation technique for​​​‌ Poisson shot noise, which‌ is a novel adaptation‌​‌ of the Chernoff technique.​​ This analytical method allows​​​‌ for the distribution of‌ the interference to be‌​‌ tightly and tractably bounded.​​ Our analysis theoretically confirms​​​‌ that the satellite sensor's‌ outage probability decreases exponentially‌​‌ as the interference constraint​​ is relaxed, and allows​​​‌ bounding of very low‌ outage probability values, which‌​‌ would be very difficult​​ to simulate.sarotte:hal-05523562

31. Subthreshold​​​‌ variability of neuronal populations‌ driven by synchronous synaptic‌​‌ inputs 1  Abstract Even​​ when driven by the​​​‌ same stimulus, neuronal responses‌ are well-known to exhibit‌​‌ a striking level of​​ spiking variability. In-vivo electrophysiological​​​‌ recordings also reveal a‌ surprisingly large degree of‌​‌ variability at the subthreshold​​ level. In prior work,​​​‌ we considered biophysically relevant‌ neuronal models to account‌​‌ for the observed magnitude​​ of membrane voltage fluctuations.​​​‌ We found that accounting‌ for these fluctuations requires‌​‌ weak but nonzero synchrony​​ in the spiking activity,​​​‌ in amount that are‌ consistent with experimentally measured‌​‌ spiking correlations. Here we​​ investigate whether such synchrony​​​‌ can explain additional statistical‌ features of the measured‌​‌ neural activity, including neuronal​​ voltage covariability and voltage​​​‌ skewness. Addressing this question‌ involves conducting a generalized‌​‌ moment analysis of conductance-based​​ neurons in response to​​​‌ input drives modeled as‌ correlated jump processes. Technically,‌​‌ we perform such an​​ analysis using fixed-point techniques​​​‌ from queuing theory that‌ are applicable in the‌​‌ stationary regime of activity.​​ We found that weak​​​‌ but nonzero synchrony can‌ consistently explain the experimentally‌​‌ reported voltage covariance and​​ skewness. This confirms the​​​‌ role of synchrony as‌ a primary driver of‌​‌ cortical variability and supports​​ that physiological neural activity​​​‌ emerges as a population-level‌ phenomenon, especially in the‌​‌ spontaneous regime. Author summary​​ Owing to the sheer​​​‌ complexity of biological networks,‌ identifying the design principles‌​‌ for neural computations will​​ only be possible via​​​‌ the simplifying lens of‌ theory. However, to be‌​‌ accepted as valid explanations,​​ theories need to be​​​‌ implemented in idealized neuronal‌ models that can reproduce‌​‌ key aspects of the​​ measured neural activity. Only​​​‌ then can these theories‌ be subjected to experimental‌​‌ validation. In this manuscript,​​ we address this requirement​​​‌ by asking: under which‌ conditions can biophysically relevant‌​‌ neuronal models reproduce physiologically​​ realistic subthreshold activity? We​​​‌ answer this question by‌ focusing on the membrane‌​‌ voltage correlation and skewness,​​ two key statistical signatures​​​‌ of the variable neuronal‌ responses that have been‌​‌ well characterized in behaving​​ mammals. As our core​​​‌ result, we show that‌ the presence of weak‌​‌ but nonzero spiking synchrony​​ is necessary to elicit​​​‌ physiological neuronal responses. The‌ identification of synchrony as‌​‌ a primary driver of​​ neural activity runs counter​​​‌ to the currently prevailing‌ asynchronous state hypothesis, which‌​‌ serves as the basis​​ for many leading neural​​​‌ network theories. Recognizing a‌ central role for synchrony‌​‌ supports that neural computations​​ fundamentally emerge at the​​​‌ collective level rather than‌ as the result of‌​‌ independent parallel processing in​​ neural circuits.

9.1 Bilateral contracts‌​‌ with industry

Participants: Bartłomiej​​​‌ Błaszczyszyn, Lucas Darlavoix​.

10.1 International​​​‌ initiatives

10.2 European initiatives

10.3 National initiatives​​​‌

10.4 Regional initiatives​​​‌

10.5 Public policy‌ support

11.1 Promoting‌​‌ scientific activities

11.2 Teaching -​​ Supervision - Juries -​​​‌ Educational and pedagogical outreach​

Exercise classes/TD, Introduction to​‌ probability, Sorbonne University (36h​​ plus correction of copies)​​​‌

11.3 Popularization

• Bartłomiej Błaszczyszyn​​ led a half-day session​​​‌ for high school students‌ as part of the‌​‌ mandatory 10th-grade (Seconde​​) internship program, June​​​‌ 2025.

12.1 Publications of the‌​‌ year

12.2 Cited publications

• 32​​​‌ articleD.David Aldous​ and R.Russell Lyons​‌. Processes on Unimodular​​ Random Networks.Electronic​​​‌ Journal of Probability12​2007, 1454 --​‌ 1508back to text​​
• 33 articleS.Siva​​​‌ Athreya, W.Wolfgang​ Löhr and A.Anita​‌ Winter. The gap​​ between Gromov-vague and Gromov--Hausdorff-vague​​​‌ topology.Stochastic Processes​ and their Applications126​‌92016, 2527--2553​​back to text
• 34​​​‌ articleE. N.Edgar​ N Gilbert. Random​‌ graphs.The Annals​​ of Mathematical Statistics30​​​‌41959, 1141--1144​back to text
• 35​‌ miscC.Christian Hirsch​​, B.Benedikt Jahnel​​​‌, S. K.Sanjoy​ Kumar Jhawar and P.​‌Péter Juhász. Poisson​​ approximation of fixed-degree nodes​​​‌ in weighted random connection​ models.February 2024​‌HALback to text​​
• 36 bookJ.Janine​​​‌ Illian, A.Antti​ Penttinen, H.Helga​‌ Stoyan and D.Dietrich​​ Stoyan. Statistical analysis​​​‌ and modelling of spatial​ point patterns.John​‌ Wiley & Sons2008​​back to text
• 37​​​‌ bookL.Leonard Kleinrock​. Communications Nets: Stochastic​‌ Message Flow and Delay​​.McGraw-Hill1964back​​​‌ to text
• 38 book​S.Stéphane Mallat.​‌ A wavelet tour of​​ signal processing.Elsevier​​​‌1999back to text​
• 39 articleA. N.​‌Aleksandr Nikolaevich Rybko and​​ S. B.Semen Bensionovich​​​‌ Shlosman. Poisson hypothesis​ for information networks. I​‌.Moscow mathematical journal​​532005,​​​‌ 679--704back to text​
• 40 articleS.Salvatore​‌ Torquato. Hyperuniform states​​ of matter.Physics​​​‌ Reports7452018,​ 1--95back to text​‌