Séminaire de Probabilités commun ICJ/UMPA

Quantitative unified framework for hydrodynamic limits

by Mrs Angeliki Menegaki

Fokko du Cloux (ICJ, Bâtiment Braconnier)
We will present a new quantitative approach to the problem of proving hydrodynamic limits from microscopic stochastic particle systems, namely the zero-range process, the simple exclusion process and the Ginzburg-Landau process with Kawasaki dynamics, to macroscopic partial differential equations. Our method combines a modulated Wasserstein-distance estimate comparing the law of the stochastic process to the local Gibbs measure, together with stability estimates a la Kruzhkov in weak distance and consistency estimates exploiting the regularity of the limit solution. It is simplified as it avoids the use of the block estimates.  This is a joint work with Daniel Marahrens and Clément Mouhot (University of Cambridge).