Abstract
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.
MSC Codes 60K35, 60K37
| Original language | English (US) |
|---|---|
| Journal | Unknown Journal |
| State | Published - May 31 2020 |
Keywords
- Brox diffusion,
- Hydrodynamic,
- Interacting particle system,
- Quasilinear
- Sinai random environment,
- SPDE,
- Zero-range,
ASJC Scopus subject areas
- General