Quantitative framework for hydrodynamic limits

Menegaki Angeliki, Imperial College London

We will present a new quantitative approach to the problem of proving hydrodynamic limits from microscopic stochastic particle systems, namely the zero-range, the simple exclusion 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 Clément Mouhot (University of Cambridge) and Daniel Marahrens.

Area: CS43 - Hydrodynamic limits (Simone Floreani)

Keywords: Quantitiative Hydrodynamical limit, Interacting particle systems

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