A consistence-stability approach to hydrodynamic limit of interacting particle systems on lattices
Menegaki, Angeliki1 ; Mouhot, Clément2
1 Institut des hautes études Scientifiques, 35 Rte de Chartres, 91440, Bures-sur-Yvette, France
2 Department of Pure Mathematics and Mathematical Statistics, University of Cambridge Wilberforce Road, CB3 0WA Cambridge, UK
Séminaire Laurent Schwartz — EDP et applications (2021-2022), Exposé no. 7, 15 p.

This is a review based on the presentation done at the seminar Laurent Schwartz in December 2021. It is announcing results in the forthcoming [MMM22]. 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 both the so-called “block estimates”.

Publié le :
DOI : 10.5802/slsedp.154
Menegaki, Angeliki 1 ; Mouhot, Clément 2

1 Institut des hautes études Scientifiques, 35 Rte de Chartres, 91440, Bures-sur-Yvette, France
2 Department of Pure Mathematics and Mathematical Statistics, University of Cambridge Wilberforce Road, CB3 0WA Cambridge, UK 
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Menegaki, Angeliki; Mouhot, Clément. A consistence-stability approach to hydrodynamic limit of interacting particle systems on lattices. Séminaire Laurent Schwartz — EDP et applications (2021-2022), Exposé no. 7, 15 p. doi : 10.5802/slsedp.154. http://www.numdam.org/articles/10.5802/slsedp.154/

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