Exposé
GT-PTESD20231009
Monotonie d'une énergie logarithmique pour les matrices aléatoires
Dans cet exposé, je présenterai une fonctionnelle d'entropie pour la distribution spectrale empirique moyenne des matrices aléatoires qui semble être monotone selon les trois théorèmes limites classiques de Wigner, Tao-Vu et Marčenko-Pastur.
GT-PTESD20230911
Couplages gagnants de chaînes de Markov
Cet exposé est basé sur un article de David Griffeath: A maximal coupling for Markov chains, dont le sujet est le couplage de chaînes de Markov, c'est-à-dire la loi jointe de copies de la chaîne de Markov qui partent respectivement de points $i$ et $j$. Un tel couplage est considéré comme gagnant si, pour tous points de départ $i$ et $j$, les deux copies de la chaîne de Markov finissent par se rencontrer presque sûrement.
GTPSD-20230904
Quelques remarques sur le théorème ergodique pour des U-statistiques
Dans cet exposé, nous présenterons le théorème ergodique pour des U-statistiques d'ordre deux : des conditions suffisantes pour la
convergence presque sûre et dans $L^1$ ainsi que des exemples montrant que la convergence ne peut pas avoir lieu en général. Les résultats présentés
sont ceux de l'article https://arxiv.org/abs/2302.04539, réalisé en collaboration avec Herold Dehling et Dalibor Volny.
Homogenization of a monotone problem in a domain with oscillating boundary
In this talk we analyze the homogenization process of a problem studied by Dominique Blanchard, Luciano Carbone and Antonio Gaudiello. A possible approach in the case of a less regular data will also be discussed
Truncated sequential change-point detection for Markov chains with applications in the epidemic statistical analysis
We consider truncated detection problems for statistical models with dependent observations given by Bayesian Markov chains for a uniform prior distribution when the number of observations is limited by some known value.
Strategies for first-order differentiation in the space of measures
The space of measures with finite second moment, when endowed with the Wasserstein distance, is a geodesic space but not a vector space. Therefore, building an adequate differential calculus is not straightforward, and currently subject of debate in the literature. We review the main definitions in use in the Hamilton-Jacobi and Mean Fields communities, with examples illustrating the nature of the objects and comments on the range and limitations of each point of view.
GTEDPCS20230613
Stochastic Heat equation with piecewise constant coefficients
We introduce a new stochastic partial differential equation with second- order elliptic operator in divergence form, having a piecewise constant diffusion coefficient, and driven by different Gaussian noise. Such equation could be used in mathematical modeling of diffusion phenomena in medium consisting of two kinds of materials and undergoing stochastic perturbations. We prove the existence of the solution and we present explicit expressions of its covariance and variance functions.
Limits of non-local approximations to the Eikonal equation on manifolds
We consider a non-local approximation of the time-dependent Eikonal equation defined on a Riemannian manifold. We show that the local and the non-local problems are well-posed in the sense of viscosity solutions and we prove regularity properties of these solutions in time and space. If the kernel is properly scaled, we then derive error bounds between the solution of the non-local problem and the one of the local problem, both in continuous-time and Forward Euler discretization. Finally, we apply these results to a sequence of random weighted graphs with $n$ vertices.
GT-PTESD20230522
Hydrodynamic and hydrostatic limit for a generalized contact process with slow reservoirs
We consider an interacting particle system which models the sterile insect technique on a finite cylinder. When in contact with slow reservoirs , the hydrodynamic limit of the latter system is a set of coupled reaction diffusion equations with mixed boundary conditions, boundary conditions which depends on the slow-down rates of the reservoirs. The goal of this talk is to prove the existence of a hydrostatic limit for a class of parameters.