On hydrodynamic limits in Sinai-type random environments

We investigate the hydrodynamical behavior of a system of random walks with zero-range interactions moving in a common `Sinai-type' random environment on a one dimensional torus. The hydrodynamic equation found is a quasilinear SPDE with a `rough' random drift term coming from a scaling of...

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Bibliographic Details
Published inarXiv.org
Main Authors Landim, Claudio, Pacheco, Carlos G, Sethuraman, Sunder, Xue, Jianfei
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 31.05.2020
Subjects
Hydrodynamic equations
Particle interactions
Particle mass
Random walk
Toruses
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Summary:We investigate the hydrodynamical behavior of a system of random walks with zero-range interactions moving in a common `Sinai-type' random environment on a one dimensional torus. The hydrodynamic equation found is a quasilinear SPDE with a `rough' random drift term coming from a scaling of the random environment and a homogenization of the particle interaction. Part of the motivation for this work is to understand how the space-time limit of the particle mass relates to that of the known single particle Brox diffusion limit. In this respect, given the hydrodynamic limit shown, we describe formal connections through a two scale limit.
ISSN:2331-8422