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Article Dans Une Revue The Annals of Applied Probability Année : 2022

On hydrodynamic limits in Sinai-type random environments

Résumé

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.
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Dates et versions

hal-03024402 , version 1 (25-11-2020)

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Claudio Landim, Carlos Pacheco, Sunder Sethuraman, Jianfei Xue. On hydrodynamic limits in Sinai-type random environments. The Annals of Applied Probability, 2022, 33 (1), ⟨10.1214/22-AAP1813⟩. ⟨hal-03024402⟩
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