ON HYDRODYNAMIC LIMITS IN SINAI-TYPE RANDOM ENVIRONMENTS

Claudio Landim, Carlos G. Pacheco, Sunder Sethuraman, Jianfei Xue

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
JournalUnknown Journal
StatePublished - May 31 2020

Keywords

  • Brox diffusion,
  • Hydrodynamic,
  • Interacting particle system,
  • Quasilinear
  • Sinai random environment,
  • SPDE,
  • Zero-range,

ASJC Scopus subject areas

  • General

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