Publications

2026

• Non-Asymptotic Convergence of Discrete Diffusion Models: Masked and Random Walk dynamics
  
  • Conforti Giovanni
  • Durmus Alain
  • Pham Le-Tuyet-Nhi
  • Raoul Gael
  , 2025. Diffusion models for continuous state spaces based on Gaussian noising processes are now relatively well understood, as many works have focused on their theoretical analysis. In contrast, results for diffusion models on discrete state spaces remain limited and pose significant challenges, particularly due to their combinatorial structure and their more recent introduction in generative modelling. In this work, we establish new and sharp convergence guarantees for three popular discrete diffusion models (DDMs). Two of these models are designed for finite state spaces and are based respectively on the random walk and the masking process. The third DDM we consider is defined on the countably infinite space $\mathbb{N}^d$ and uses a drifted random walk as its forward process. For each of these models, the backward process can be characterized by a discrete score function that can, in principle, be estimated. However, even with perfect access to these scores, simulating the exact backward process is infeasible, and one must rely on approximations. In this work, we study Euler-type approximations and establish convergence bounds in both Kullback-Leibler divergence and total variation distance for the resulting models, under minimal assumptions on the data distribution. In particular, we show that the computational complexity of each method scales linearly in the dimension, up to logarithmic factors. Furthermore, to the best of our knowledge, this study provides the first non-asymptotic convergence guarantees for these noising processes that do not rely on boundedness assumptions on the estimated score.
• Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2 -distance
  
  • Gentiloni-Silveri Marta
  • Ocello Antonio
  , 2025. Score-based Generative Models (SGMs) aim to sample from a target distribution by learning score functions using samples perturbed by Gaussian noise. Existing convergence bounds for SGMs in the W2-distance rely on stringent assumptions about the data distribution. In this work, we present a novel framework for analyzing W2-convergence in SGMs, significantly relaxing traditional assumptions such as log-concavity and score regularity. Leveraging the regularization properties of the Ornstein-Uhlenbeck (OU) process, we show that weak log-concavity of the data distribution evolves into log-concavity over time. This transition is rigorously quantified through a PDE-based analysis of the Hamilton-Jacobi-Bellman equation governing the log-density of the forward process. Moreover, we establish that the drift of the time-reversed OU process alternates between contractive and noncontractive regimes, reflecting the dynamics of concavity. Our approach circumvents the need for stringent regularity conditions on the score function and its estimators, relying instead on milder, more practical assumptions. We demonstrate the wide applicability of this framework through explicit computations on Gaussian mixture models, illustrating its versatility and potential for broader classes of data distributions.
• A functional inequalities approach for the field-road diffusion model with (symmetric) nonlinear exchanges
  
  • Alfaro Matthieu
  • Chainais-Hillairet Claire
  • Nabet Flore
  , 2026. In this note, we consider the so-called field-road diffusion model in a bounded domain, consisting of two parabolic PDEs posed on sets of different dimensions and coupled through (symmetric) nonlinear exchange terms. We propose a new and rather direct functional inequalities approach to prove the exponential decay of a relative entropy, and thus the convergence of the solution towards the stationary state selected by the total mass of the initial datum.
• Subadditivity and optimal matching of unbounded samples
  
  • Caglioti Emanuele
  • Goldman Michael
  • Pieroni Francesca
  • Trevisan Dario
  , 2026. We obtain new bounds for the optimal matching cost for empirical measures with unbounded support. For a large class of radially symmetric and rapidly decaying probability laws, we prove for the first time the asymptotic rate of convergence for the whole range of power exponents $p$ and dimensions $d$. Moreover we identify the exact prefactor when $p\le d$. We cover in particular the Gaussian case, going far beyond the currently known bounds. Our proof technique is based on approximate sub- and super-additivity bounds along a geometric decomposition adapted to some features the density, such as its radial symmetry and its decay at infinity.
• Long-time behaviour of a multidimensional age-dependent branching process with a singular jump kernel modelling telomere shortening
  
  • Olayé Jules
  • Tomasevic Milica
  Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2026, 31. In this article, we investigate the ergodic behaviour of a multidimensional age-dependent branching process with a singular jump kernel, motivated by studying the phenomenon of telomere shortening in cell populations. Our model tracks individuals evolving within a continuous-time framework indexed by a binary tree, characterised by age and a multidimensional trait. Branching events occur with rates dependent on age, where offspring inherit traits from their parent with random increase or decrease in some coordinates, while the most of them are left unchanged. Exponential ergodicity is obtained at the cost of an exponential normalisation, despite the fact that we have an unbounded age-dependent birth rate that may depend on the multidimensional trait, and a non-compact transition kernel. These two difficulties are respectively treated by stochastically comparing our model to Bellman-Harris processes, and by using a weak form of a Harnack inequality. We conclude this study by giving examples where the assumptions of our main result are verified. (10.1214/25-EJP1469)
  DOI : 10.1214/25-EJP1469
• Proving symmetry of localized solutions and application to dihedral patterns in the planar Swift-Hohenberg PDE
  
  • Blanco Dominic
  • Cadiot Matthieu
  , 2026. <div><p>In this article, we extend the framework developed in [14] to allow for rigorous proofs of existence of smooth, localized solutions in semi-linear partial differential equations possessing both space and non-space group symmetries. We demonstrate our approach on the Swift-Hohenberg model. In particular, for a given symmetry group G, we construct a natural Hilbert space H l G containing only functions with G-symmetry. In this space, products and differential operators are well-defined allowing for the study of autonomous semi-linear PDEs. Depending on the properties of G, we derive a Newton-Kantorovich approach based on the construction of an approximate inverse around an approximate solution, u0. More specifically, combining a meticulous analysis and computer-assisted techniques, the Newton-Kantorovich approach is validated thanks to the computation of some explicit bounds. The strategy for constructing u0, the approximate inverse, and the computation of these bounds will depend on the properties of G and its maximal square lattice space subgroup, H. More specifically, we consider three cases: G is a space group which can be represented on the square lattice, G is not a space group which can be represented on the square lattice and the symmetry of H isolates the solution, and where G is not a space group which can be represented on the square lattice and the symmetry of H does not isolate the solution. We demonstrate the methodology on the 2D Swift-Hohenberg PDE by proving the existence of various dihedral localized patterns. The algorithmic details to perform the computer-assisted proofs can be found on Github [4].</p></div>
• Existence and orbital stability proofs of traveling wave solutions on an infinite strip for the suspension bridge equation
  
  • van der Aalst Lindsey
  • Cadiot Matthieu
  , 2026. <div><p>In this paper, we present a computer-assisted approach for constructively proving the existence of traveling wave solutions of the suspension bridge equation on the infinite strip Ω = R × (-d2, d2). Using a meticulous Fourier analysis, we derive a quantifiable approximate inverse A for the Jacobian DF(ū) of the PDE at an approximate traveling wave solution ū. Such approximate objects are obtained thanks to Fourier coefficient sequences and operators, arising from Fourier series expansions on a rectangle Ω0 = (-d1, d1) × (-d2, d2) for large d1. In particular, the challenging exponential nonlinearity of the equation is tackled using a rigorous control of the aliasing error when computing related Fourier coefficients. This allows to establish a Newton-Kantorovich approach, from which the existence of a true traveling wave solution of the PDE can be proven in a vicinity of ū. We successfully apply such a methodology in the case of the suspension bridge equation and prove the existence of multiple traveling wave solutions on Ω. Finally, given a proven solution ũ, a Fourier series approximation on Ω0 allows us to accurately enclose the spectrum of DF(ũ). Such a tight control provides the number of negative eigenvalues, which in turn, allows us to conclude about the orbital (in)stability of the traveling wave.</p></div>
• Proving the existence of localized patterns and saddle node bifurcations in 1D activator-inhibitor type models
  
  • Blanco Dominic
  • Cadiot Matthieu
  • Fassler Daniel
  , 2026. <div><p>In this paper, we present a general framework for constructively proving the existence and stability of stationary localized 1D solutions and saddle-node bifurcations in activatorinhibitor systems using computer-assisted proofs. Specifically, we develop the necessary analysis to compute explicit upper bounds required in a Newton-Kantorovich approach. Given an approximate solution ū, this approach relies on establishing that a well-chosen fixed point map is contracting on a neighborhood ū. For this matter, we construct an approximate inverse of the linearization around ū, and establish sufficient conditions under which the contraction is achieved. This provides a framework for which computer-assisted analysis can be applied to verify the existence and local uniqueness of solutions in a vicinity of ū, and control the linearization around ū. Furthermore, we extend the method to rigorously establish saddle-node bifurcations of localized solutions for the same type of models, by considering a well-chosen zero-finding problem. This depends on the rigorous control of the spectrum of the linearization around the bifurcation point. Finally, we demonstrate the effectiveness of the framework by proving the existence and stability of multiple steady-state patterns in various activatorinhibitor systems, as well as a saddle-node bifurcation in the Glycolysis model.</p></div>
• Separation rates for the detection of synchronization of interacting point processes in a mean field frame. Application to neuroscience.
  
  • Tchouanti Josué
  • Löcherbach Éva
  • Reynaud-Bouret Patricia
  • Tanré Etienne
  Electronic Journal of Statistics, Shaker Heights, OH : Institute of Mathematical Statistics, 2026, 20 (1), pp.560--632. Permutation tests have been proposed by Albert et al. (2015) to detect dependence between point processes, modeling in particular spike trains, that is the time occurrences of action potentials emitted by neurons. Our present work focuses on exhibiting a criterion on the separation rate to ensure that the Type II errors of these tests are controlled non asymptotically. This criterion is then discussed in two major models in neuroscience: the jittering Poisson model and Hawkes processes having \(M\) components interacting in a mean field frame and evolving in stationary regime. For both models, we obtain a lower bound of the size \(n\) of the sample necessary to detect the dependency between two neurons. (10.1214/26-EJS2483)
  DOI : 10.1214/26-EJS2483
• Finite element modelling for the reproduction of dynamic OCE measurements in the cornea
  
  • Merlini Giulia
  • Imperiale Sébastien
  • Allain Jean-Marc
  Journal of the Mechanics and Physics of Solids, Elsevier, 2026, 206, pp.106363. Recent advances in dynamic elastography, particularly through optical coherence tomography combined with transient excitations have enabled rapid, localized, and non-invasive mechanical data acquisition of the cornea. This dataopens the path to early-detection of pathologies and more accurate treatment. However, the analysis of the wave propagation is a complex mechanical problem: the cornea is a structure under pressure, with non-linear material behavior. Thus, computational analysis are needed to extract mechanical parameters from the data. In this study, we present a time-dependent finite element model for the reproduction of transient shear wave elastographic measurements in the cornea. The mechanical problem consists in a smallamplitude wave propagating in the cornea, largely deformed by intraocular pressure in physiological conditions. The model accounts for anisotropic, hyperelastic, and incompressible behavior of the cornea, as well as its accurate geometry, and the preloaded condition. We have implemented two different numerical approaches to solve first the static non-linear inflation of the cornea and then the linear wave propagation problem to reproduce the measurements. We investigate the impact of material anisotropy and prestress on wave propagation and demonstrate that intraocular pressure critically influences shear wave velocity. Additionally, by introducing a localized mechanical defect to simulate a pathological defect, we show that simulated shear wave can detect and quantify mechanical weaknesses, suggesting potential as a diagnostic tool to assess corneal health. (10.1016/j.jmps.2025.106363)
  DOI : 10.1016/j.jmps.2025.106363
• Self-interacting approximation to McKean-Vlasov long-time limit: a Markov chain Monte Carlo method
  
  • Du Kai
  • Ren Zhenjie
  • Suciu Florin
  • Wang Songbo
  Journal de Mathématiques Pures et Appliquées, Elsevier, 2026, 205, pp.103782. For a certain class of McKean-Vlasov processes, we introduce proxy processes that substitute the mean-field interaction with self-interaction, employing a weighted occupation measure. Our study encompasses two key achievements. First, we demonstrate the ergodicity of the self-interacting dynamics, under broad conditions, by applying the reflection coupling method. Second, in scenarios where the drifts are negative intrinsic gradients of convex mean-field potential functionals, we use entropy and functional inequalities to demonstrate that the stationary measures of the self-interacting processes approximate the invariant measures of the corresponding McKean-Vlasov processes. As an application, we show how to learn the optimal weights of a two-layer neural network by training a single neuron. (10.1016/j.matpur.2025.103782)
  DOI : 10.1016/j.matpur.2025.103782
• Counterfactually Fair Regression via Optimal Transport
  
  • Lince Marie Generali
  • Gaucher Solenne
  • Vie Jill-Jênn
  • Loiseau Patrick
  , 2026. We consider the problem of learning a counterfactually fair regressor. We adopt a causal uncertainty view in which counterfactual fairness is defined with resampled noise. We focus on obtaining theoretical fairness guarantees for a new post-processing estimator. We begin by showing that counterfactual fairness is equivalent to satisfying demographic parity conditional on the latent variable. This allows us to provide a closed-form expression of the optimal fair regressor via a barycentric quantile map. In order to handle continuous latent variables, we propose a discretized post-processing method. Then, under mild regularity assumptions, we prove high-probability finite-sample fairness guarantees for our estimator, providing an unfairness decay at rate Õ(n -1/3 ), and establishing a matching risk bound of order Õ(n -1/3 ). We provide a matching lower bound on the excess risk of almost fair predictions. Finally, we extend our results to the setting of relaxed counterfactual fairness. We validate our approach on real-world and synthetic data.
• Évaluation de l'équilibre électrique du scénario négawatt 2022 à l'aide du modèle open source eoles
  
  • Cédiey Hippolyte
  • Quirion Philippe
  • Baratgin Laure
  • Bustarret Quentin
  • de Oliveira-Gill Nilam
  • Perrier Quentin
  • Escribe Célia
  • Letz Thomas
  • Salomon Thierry
  • Shirizadeh Behrang
  Revue de l'OFCE, Presses de Sciences Po, 2026. Nous présentons la dernière version du modèle d'optimisation du système énergétique open source Eoles et nous l'utilisons pour évaluer dans quelle mesure le mix énergétique du scénario négaWatt 2022 peut satisfaire la demande d'énergie en France à l'horizon 2050, pour 19 années météorologiques. Nous obtenons que même sans recours aux interconnexions, la demande d'électricité n'excède la production que 3 à 4 heures par an en moyenne, ce qui ne dépasse que de très peu les critères de défaillance du Code de l'énergie. Pour éliminer toute heure de défaillance et assurer les besoins de réserves, une puissance supplémentaire de technologies pilotables de 13,8 GW est nécessaire, soit une augmentation de 39 % par rapport au scénario négaWatt. Nous étudions l'ajout de trois technologies pilotables : turbines à gaz (méthane ou hydrogène) et batteries, qui sont toutes proches en termes de coût total du système énergétique. Par ailleurs, l'équilibre électrique peut être atteint même en réduisant la capacité photovoltaïque sur toitures par rapport au scénario négaWatt. Le gain associé (3,4 Md€/an) est plus élevé que le surcoût entraîné par les capacités pilotables mentionnées ci-dessus (environ 1 Md€/an).
• Covariance-Informed Subspace: an Adaptive Gradient-Free Input Dimension Reduction Method for Bayesian Inference
  
  • Polette Nadège
  • Le Maître Olivier
  • Sochala Pierre
  • Gesret Alexandrine
  , 2026. This paper addresses the challenge of dimension reduction (DR) in Bayesian inference of high-resolution two-or three-dimensional fields, where a priori parametrizations require a large number of terms. The underlying idea is common to state-of-the-art methods in which the parameter space is decomposed into two subspaces, one informed by the likelihood and one constrained by the prior. DR techniques generally use gradient information from the log-likelihood to derive the corresponding subspaces. However, the gradient may be unavailable or expensive to compute accurately, for instance in the case of simulation-based inference. Inspired by approaches based on likelihood-informed subspaces, we develop a new DR method tailored for settings where gradient computation is not feasible. More specifically, we propose a gradient-free indicator for determining whether a direction is informed by the data. This indicator is derived from the posterior-to-prior covariance ratio introduced in Spantini et al. (2015). We show that, in the linear Gaussian case, this indicator combined with an approximate likelihood leads to a better posterior approximation. The method is then extended to nonlinear cases, and strategies to approximate the posterior covariance are detailed. We demonstrate the effectiveness of this DR through two high-dimensional inference problems arising from groundwater and atmospheric applications.
• ExceedGAN: Simulation above extreme thresholds using Generative Adversarial Networks
  
  • Allouche Michaël
  • Girard Stéphane
  • Gobet Emmanuel
  Extremes, Springer Verlag (Germany), 2026. This paper devises a novel neural-inspired approach for simulating multivariate extremes. Specifically, we propose a GAN-based generative model for sampling multivariate data exceeding large thresholds, giving rise to what we refer to as the ExceedGAN algorithm. Our approach is based on approximating marginal log-quantile functions using feedforward neural networks with eLU activation functions specifically introduced for bias correction. An error bound is provided {on the margins}, assuming a $J$th order condition from extreme value theory. The numerical experiments illustrate that ExceedGAN outperforms competitors, both on synthetic and real-world data sets. The code is available at \url{https://github.com/michael-allouche/extreme-value-GAN} (10.1007/s10687-026-00528-9)
  DOI : 10.1007/s10687-026-00528-9
• A REMARK ON SELF-ADJOINT PROBLEMS IN THE OPTIMIZATION OF NON-LINEAR MODELS
  
  • Égoire Allaire G R
  • Cherrière Théodore
  • Gauthey Thomas
  • Hage Hassan Maya
  • Mininger Xavier
  Journal of Optimization Theory and Applications, Springer Verlag, 2026, 208, pp.100. This article considers optimization problems under nonlinear partial differential equation (p.d.e.) constraints. It is assumed that the p.d.e. arises from minimizing a convex energy. We prove that the optimization problem is self-adjoint when the objective function is the dual energy. In other words, the differential of the objective function with respect to the optimization variable does not involve any adjoint state. This result generalizes the well-known fact that the so-called compliance is self-adjoint in the linear case. We also prove that in a large class of objective functions the dual energy is the only one which is self-adjoint.
• Hybrid FEM/IPDG semi-implicit schemes for time domain electromagnetic wave propagation in non cylindrical coaxial cables
  
  • Beni Hamad Akram
  • Imperiale Sébastien
  • Joly Patrick
  ESAIM: Mathematical Modelling and Numerical Analysis, Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP, 2026. In this work, we develop an efficient numerical method for solving 3D Maxwell's equations in non-cylindrical coaxial cables. The main challenge arises from the elongated geometry of the computational domain, which induces strong anisotropy between the longitudinal direction (along the cable) and the transverse directions (within the cross-sections). This leads to the use of highly anisotropic meshes, where the longitudinal mesh size is much larger than the transverse one.<p>Our objective is to design a numerical scheme that is explicit in the longitudinal direction, with a CFL stability condition depending only on the longitudinal mesh size. In a previous work, we achieved this for cylindrical cables by employing prismatic edge elements, 1D quadrature for longitudinal mass lumping, and a hybrid explicit/implicit time discretization. The present paper extends this approach to non-cylindrical cables, addressing several new difficulties with the following key ingredients: (1) representing the cable as a deformation of a reference cylindrical cable and employing mapping techniques between the physical and reference domains; (2) using an anisotropic space discretization that combines an interior penalty discontinuous Galerkin (IPDG) method in the transverse directions with a conforming finite element method in the longitudinal direction; (3) utilizing prismatic edge elements on a prismatic mesh of the reference cable; and (4) adapting the construction of the hybrid explicit-implicit time discretization to the new structure of the semidiscrete problem. From a theoretical perspective, the main difficulty lies in the stability analysis, which requires extending and adapting standard techniques for DG methods in space and energy methods in time.</p>
• Nonlinear model calibration through bifurcation curves
  
  • Mélot Adrien
  • Denimal Goy Enora
  • Renson Ludovic
  Mechanical Systems and Signal Processing, Elsevier, 2026, 242, pp.113589. Nonlinear systems exhibit a plethora of complex dynamic behaviours that are difficult to model and predict accurately. This difficulty often arises from a lack of knowledge of the physics that induces the nonlinear behaviours and the strong sensitivity of the nonlinear dynamics to parameter variation. We introduce in this paper a methodology to carry out nonlinear model updating based on bifurcations. The proposed approach involves minimising the distance between experimental and numerical bifurcation curves, which are key dynamic features that define stability boundaries and regions of multi-stability. For the model, bifurcation curves are computed via standard numerical bifurcation tracking analyses. In the experiment, we use control-based continuation to obtain the data. The approach is first demonstrated on a Duffing and a beam system using synthetic data, before being applied to experimental data collected on a base-excited energy harvester with magnetic nonlinearity.
• Improved well-posedness for the limit flow of differentiation of roots of polynomials
  
  • Bertucci Charles
  • Pesce Valentin
  , 2026. In this paper, we study the partial differential equation on the circle that was heuristically obtained by Steinerberg [32] on the real line and which represents the evolution of the density of the roots of polynomials under differentiation. After integrating the partial differential equation in question, we observe that it can be treated with the theory of viscosity solutions. This equation at hand is a non linear parabolic integro-differential equation which involves the elliptic operator called the half-Laplacian. Due to the singularity of the equation, we restrict our study to strictly positive initial condition. We obtain a comparison principle for solutions of the primitive equation which yields uniqueness, existence, continuity with respect to initial condition. We also present heuristics to justify that the system of particles indeed approximates the solution of the equation.
• A stochastic use of the Kurdyka-Lojasiewicz property: Investigation of optimization algorithms behaviours in a non-convex differentiable framework
  
  • Fest Jean-Baptiste
  • Repetti Audrey
  • Chouzenoux Emilie
  Foundations of Data Science, American Institute of Mathematical Sciences, 2026, 9, pp.164-191. Asymptotic analysis of generic stochastic algorithms often relies on descent conditions. In a convex setting, some technical shortcuts can be considered to establish asymptotic convergence guarantees of the associated scheme. However, in a non-convex setting, obtaining similar guarantees is usually more complicated, and relies on the use of the Kurdyka-Łojasiewicz (KŁ) property. While this tool has become popular in the field of deterministic optimization, it is much less widespread in the stochastic context and the few works making use of it are essentially based on trajectory-by-trajectory approaches. In this paper, we propose a new framework for using the KŁ property in a non-convex stochastic setting based on conditioning theory. We show that this framework allows for deeper asymptotic investigations on stochastic schemes verifying some generic descent conditions. We further show that our methodology can be used to prove convergence of generic stochastic gradient descent (SGD) schemes, and unifies conditions investigated in multiple articles of the literature. (10.3934/fods.2025016)
  DOI : 10.3934/fods.2025016
• Stability analysis of a new curl-based full field reconstruction method in 2D isotropic nearly-incompressible elasticity
  
  • Chibli Nagham
  • Genet Martin
  • Imperiale Sébastien
  Inverse Problems, IOP Publishing, 2026. In time-harmonic elastography, the shear modulus is typically inferred from full field displacement data by solving an inverse problem based on the time-harmonic elastodynamic equation. In this paper, we focus on nearly incompressible media, which pose robustness challenges, especially in the presence of noisy data. Restricting ourselves to 2D and considering an isotropic, linearly deforming medium, we reformulate the problem as a non-autonomous hyperbolic system and, through theoretical analysis, establish existence, uniqueness, and stability of the inverse problem. To ensure robustness with noisy data, we propose a least-squares approach with regularization. The convergence properties of the method are verified numerically using in silico data.
• Modelling of relative velocity, velocity fluctuations and their interactions for two-fluid models by Stationary Action Principle
  
  • Haegeman Ward
  • Orlando Giuseppe
  • Kokh Samuel
  • Massot Marc
  ESAIM: Proceedings and Surveys, EDP Sciences, 2026. The objective of this contribution is the derivation of a two-fluid model including a relative velocity between the two phases and velocity fluctuations, describing pseudo-turbulent effects, as internal variables based on Stationary Action Principle. The variational derivation, used to obtain the model, relies on the variation of a single trajectory related to the mass-weighted average velocity under the barotropic assumption. The model is hyperbolic, satisfies a second principle of thermodynamics, and admits either linearly degenerate or genuinely nonlinear characteristic fields. Moreover, the variational approach yields a fully closed model and its non-conservative products are uniquely defined for weak solutions in 1D, i.e. jump conditions can be derived. In the laminar case, when velocity fluctuations are negligible, we recover previously derived multi-fluid models which have been analyzed in several contributions. As such, the present framework allows for an original extension of the existing models to include velocity fluctuations of each phase for pseudo-turbulent flows, their coupling with the relative velocity between phases, as well as dissipative effects compatible with the thermodynamics of irreversible processes. Eventually, we provide a discussion of the limitations of the proposed model, especially regarding the extension to the open problem of non-barotropic flows.
• Spatio-temporal thermalization and adiabatic cooling of guided light waves
  
  • Zanaglia Lucas
  • Garnier Josselin
  • Carusotto Iacopo
  • Doya Valérie
  • Michel Claire
  • Picozzi Antonio
  Physical Review Letters, American Physical Society, 2026, 136, pp.053802. We propose and theoretically characterize three-dimensional spatio-temporal thermalization of a continuous-wave classical light beam propagating along a multi-mode optical waveguide. By combining a non-equilibrium kinetic approach based on the wave turbulence theory and numerical simulations of the field equations, we anticipate that thermalizing scattering events are dramatically accelerated by the combination of strong transverse confinement with the continuous nature of the temporal degrees of freedom. In connection with the blackbody catastrophe, the thermalization of the classical field in the continuous temporal direction provides a novel intrinsic mechanism for adiabatic cooling and spatial beam condensation. This process of adiabatic cooling is distinct from other mechanisms of thermalization and provides new insights into the dynamics of far-from-equilibrium closed systems and their route to thermalization. (10.1103/mqzh-w2gh)
  DOI : 10.1103/mqzh-w2gh
• Nonparametric regression on Riemannian manifolds under an alpha -mixing process
  
  • Wiem Nefzi
  • Salah Khardani
  • Françoise Yao Anne
  Communications in Statistics - Theory and Methods, Taylor & Francis, 2026, pp.1-16. This paper investigates the asymptotic properties of a kernel estimator of the regression function linking a real-valued response Y to a covariate X taking values in a Riemannian submanifold M. The estimator is an adaptation of the nonparametric regression estimator introduced by Pelletier (2006) for i.i.d. data on manifolds to the case where the observations (X t , Y t ) t∈Z form a stationary α-mixing process. Under suitable geometric regularity and mixing assumptions, we derive explicit expressions for the bias and the variance of the estimator, obtain the optimal bandwidth that minimizes the mean squared error, and establish the optimal rate of convergence in mean squared error. As a consequence, we prove both pointwise and uniform convergence in probability of the estimator on compact Riemannian manifolds under dependence. (10.1080/03610926.2026.2618625)
  DOI : 10.1080/03610926.2026.2618625
• Quantitative sensitivity analysis for Fokker-Planck equation with respect to the Wasserstein distance
  
  • Morange Martin
  , 2026. We analyze the sensitivity of solutions to the Fokker-Planck equation with respect to some unknown parameter. Our main result is to provide quantitative upper bounds for the $p$-Wasserstein distance $\mathcal{W}_p$ between two solutions with different parameters, for every $p \geq 2$. We are able to give two proofs of this result, the first relying on synchronous coupling between two solutions of an SDE, and another one that relies on the differentiation of Kantorovitch dual formulation of optimal transport. We also provide more specific bounds in the case of the overdamped Langevin process, for which we are able to compare convergence to the invariant measure and sensitivity to the parameter.