A consistence-stability approach to hydrodynamic limit of interacting particle systems on lattices

DOI10.5802/SLSEDP.154arXiv2212.00079MaRDI QIDQ6419133

Publication date: 30 November 2022

Abstract: This is a review based on the presentation done at the seminar Laurent Schwartz in December 2021. It is announcing results in the forthcoming [Menegaki-Mouhot-Marahrens'22]. This work presents a new simple quantitative method for proving the hydrodynamic limit of a class of interacting particle systems on lattices. We present here this method in a simplified setting, for the zero-range process and the Ginzburg-Landau process with Kawasaki dynamics, in the parabolic scaling and in dimension

1

. The rate of convergence is quantitative and uniform in time. The proof relies on a consistence-stability approach in Wasserstein distance, and it avoids the use of the ``block estimates.

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Stability in context of PDEs (35B35) Gas dynamics (general theory) (76N15) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Statistical mechanics of gases (82D05) Ginzburg-Landau equations (35Q56) PDEs in connection with statistical mechanics (35Q82)

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