Séminaire Analyse-Proba (Kohei Hayashi, mardi 12 mai 2026)

Le prochain séminaire Analyse-Proba aura lieu mardi 12 mai à 10h30 en A711. Kohei Hayashi (Osaka University) nous parlera de :

Degree-preserving processes and their hydrodynamics 

Abstract
We consider a class of large-scale interacting systems with one conservation law satisfying the “degree-preserving property”, and study the classification of their invariant measures and their hydrodynamic limits. Under a few basic conditions, we show that if the generator of the process preserves the degree of polynomials of the state variables up to two, then the marginals of any product invariant measure of the process must belong to one of six specific distributions, which is called the Morris class. In particular, we introduce a new model whose invariant measure is given by the generalized hyperbolic secant distribution. Additionally, under the same conditions, we show that the classical heat equation is always derived as the hydrodynamic limit equation from generic degree-preserving processes. 

This talk is based on a joint work with C. Francheschini, P. Gonçalves and M. Sasada.