Séminaire du Pôle Probabilités

Lieu : nouvelle salle de conférence du CMAP (salle 3005, dernier étage, aile 05 - soit le long couloir perpendiculaire à l’aile 0)

Horaire : un mardi sur deux, de 10h à 11h

Remarque : aux mêmes dates et dans la même salle, à 11h30, a lieu le séminaire du pôle Analyse.

Les organisateurs : Quentin Cormier, Stefano De Marco, Fabrice Djete & Charlotte Dion-Blanc.
(à contacter à l'alias orga-seminaire-pole-proba "at" meslistes.polytechnique.fr)

Prochaines séances :

Mardi 7 octobre : Guillaume Dubach (CMLS) - Powers of Ginibre matrices and cycles of commutators

The eigenvalues of the complex Ginibre ensemble (matrices with i.i.d. complex Gaussian entries) form a highly correlated system of points; however, their high powers are distributed exactly as if they were independent. I will present a consequence of this counter-intuitive property to random permutations; more specifically, we will explicitly describe the distribution of the number of cycles in a commutator between a random (uniform) permutation and another permutation with prescribed cycle type.

Mardi 21 octobre : Mattia Martini (CMAP) - Randomized Approach to Mean Field Control

This talk aims to show how randomizing the dynamics in mean field control can help regularize the associated Hamilton–Jacobi equation. A key challenge in this approach lies in constructing a suitable notion of noise on the space of probability measures. To this end, we rely on Dirichlet–Ferguson processes, as studied by Dello-Schiavo. We first examine the effect of this noise on a system of uncontrolled interacting particles and show that it induces a regularizing effect at the level of the corresponding backward Kolmogorov equation. We then analyze a mean field control problem driven by this noise and prove that the associated Hamilton–Jacobi equation admits a unique solution in an appropriate functional space, even when the coefficients have limited regularity. The talk is based on a joint work with F. Delarue (Nice) and G. Sodini (Vienna).

Mardi 4 novembre : Emma Hubert (Paris Dauphine)

Mardi 18 novembre : Cédric Boutillier (LPSM) - Domino tilings of the Aztec diamonds

Domino tilings, and more generally dimer models, are models of 2-dimensional statistical mechanics which can be studied with a large variety of techniques: determinant point processes, representation theory and symmetric functions, lattice paths, discrete geometry etc. They exhibit phase transitions which can be analyzed very precisely with all these tools. In this talk, I will review old and new results about domino tilings of a particular family of regions, called the Aztec diamonds, for which additional combinatorics properties imply even more precise probabilistic understanding. Some of these "new" results come from a recent joint work with Béatrice de Tilière.

Mardi 2 décembre : Djalil Chafaï (CEREMADE, Paris Dauphine; DMA, ENS)- Aspects of the Cutoff Phenomenon for Diffusions

The cutoff phenomenon, conceptualized in the context of finite Markov chains, states that for certain evolution equations, started from a point, the distance towards a long time equilibrium may become more and more abrupt in high dimensional state spaces and for certain choices of initial conditions. This can be seen as a critical competition between trend to equilibrium and initial condition. This talk is about the cutoff phenomenon for a few classes of linear and nonlinear diffusions. This is about joint works with Jeanne Boursier, and Cyril Labbé, with Max Fathi, and with Max Fathi and Nikita Simonov.

Mardi 16 décembre : Elisa Marini (Paris Dauphine) - Noise-induced oscillations for the mean-field dissipative contact process

In this talk, we will introduce a dissipative version of the contact process with mean-field interaction admitting a simple epidemiological interpretation. In particular, we will focus on the thermodynamic limit of the process, providing a law of large numbers (propagation of chaos) and a central limit theorem for the corresponding normal fluctuations. These results reveal that it is the noise, which is only present in the finite-size system and is internal to the system, that induces persistent oscillatory behaviors reminiscent of the emergence of pandemic waves in real epidemics.

The talk is based on a joint work with Paolo Dai Pra (University of Verona).

Mardi 13 janvier

Mardi 27 janvier

Mardi 10 février

Mardi 24 février

Mardi 10 mars

Mardi 24 mars

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Anciens séminaires

2024-2025

Mardi 24 juin : Charlotte Dion-Blanc (Sorbonne Université) - Nonparametric Estimation for Hawkes Diffusion Systems

Mardi 10 juin : Clément Foucart (Université Sorbonne Paris Nord) - Processus de branchement avec compétition en temps et espace continus et conditionnement à la non-extinction

Mardi 27 mai : Ahmed Kebaier (Université d'Evry) Approximation of Stochastic Volterra Équations with kernels of completely monotone type.

Mardi 29 avril : Pierre Le Bris (IHES) : On uniform in time propagation of chaos in the metastable Curie-Weiss model

Mardi 15 Avril : Nicolas Champagnat (Inria Nancy) - Convergence vers l'équation canonique de la dynamique adaptative d'un modèle individu-centré dans un régime de mutations petites mais fréquentes

Mardi 1 avril : Laurent Ménard (Modal'X, Paris Nanterre) - Mariages unimodulaires optimaux

Mardi 18 mars : Arvind Singh (LMO, Université-Paris-Saclay) - Jeu de Penney et jeu de Litt

Mardi 04 mars : Huyên Pham (CMAP) - Control of large-scale heterogeneous systems: an extended graphon mean-field approach

Mardi 04 février : Emmanuel Schertzer (University of Vienna) - Principe d'invariance en génétique des populations

Mardi 21 janvier : Guilherme Ost (Univ. Federal do Rio de Janeiro) - Binary graphical models with mean-field interactions: community detection and dependence graph density estimation

Mardi 07 janvier : Eva Loecherbach (Univ Paris 1) - Propagation du chaos conditionnelle pour des systèmes de particules avec des sauts stables

Mardi 17 décembre : Paul Gassiat (Paris Dauphine) - Un flot de gradient sur l'espace des contrôles avec condition initiale irrégulière

Mardi 03 décembre : Mehdi Talbi (Univ. Paris Cité) - Control of Volterra-type dynamics and applications to contract theory

Mardi 19 Novembre : Marek Kimmel (Rice University, Houston, Etats-Unis) - Estimating Past Events in Cancer Through Stochastic Modeling of DNA Sequencing Data

Mardi 5 Novembre : Arno Siri-Jégousse (UNAM Mexique) - Évolution et généalogies de populations autosimilaires

Mardi 22 Octobre : Michael Goldman (CMAP) - Recent progress on the optimal matching problem