A quantitative hydrodynamic limit of the Kawasaki dynamics

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2024Embargo end date: 01 Jul 2018Publisher:Institute of Mathematical StatisticsJournal:Electronic Journal of Probability, volume 29 (issn: 1083-6489,

Copyright policy )Funded by:NSF | Large Scale Phenomena in ...

Authors: Dizdar, Deniz; Menz, Georg; Otto, Felix; Wu, Tianqi;

doi: 10.1214/24-ejp1248 , 10.48550/arxiv.1807.09850

arXiv: 1807.09850

A quantitative hydrodynamic limit of the Kawasaki dynamics

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Abstract

We derive for the first time in the literature a rate of convergence in the hydrodynamic limit of the Kawasaki dynamics for a one-dimensional lattice system. We use an adaptation of the two-scale approach. The main difference to the original two-scale approach is that the observables on the mesoscopic level are described by a projection onto splines of second order, and not by a projection onto piecewise constant functions. This allows us to use a more natural definition of the mesoscopic dynamics, which yields a better rate of convergence than the original two-scale approach.

37 pages

Related Organizations

University of California, Los Angeles
United States
University of Montreal
Canada
Max Planck Society
Germany
Max Planck Institute for Mathematics in the Sciences
Germany

Keywords

Probability (math.PR), Primary 60K35, secondary 60J25, 82B21, FOS: Physical sciences, Interacting random processes; statistical mechanics type models; percolation theory, Kawasaki dynamics, Mathematical Physics (math-ph), Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics, two-scale approach, logarithmic Sobolev inequality, Galerkin approximation, Mathematics - Analysis of PDEs, hydrodynamic limit, FOS: Mathematics, Continuous-time Markov processes on general state spaces, Interacting particle systems in time-dependent statistical mechanics, Mathematics - Probability, Mathematical Physics, Analysis of PDEs (math.AP)

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