On hydrodynamic limits in Sinaitype random environments
Abstract
We investigate the hydrodynamical behavior of a system of random walks with zerorange interactions moving in a common `Sinaitype' 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 spacetime 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 DOI:
 10.48550/arXiv.2006.00583
 arXiv:
 arXiv:2006.00583
 Bibcode:
 2020arXiv200600583L
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 60K35;
 60K37
 EPrint:
 30 pages