Symmetric simple exclusion process in dynamic environment: Hydrodynamics

Frank Redig, Ellen Saada, Federico Sau

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Abstract

We consider the symmetric simple exclusion process in Zd with quenched bounded dynamic random conductances and prove its hydrodynamic limit in path space. The main tool is the connection, due to the self-duality of the process, between the invariance principle for single particles starting from all points and the macroscopic behavior of the density field. While the hydrodynamic limit at fixed macroscopic times is obtained via a generalization to the time-inhomogeneous context of the strategy introduced in [41], in order to prove tightness for the sequence of empirical density fields we develop a new criterion based on the notion of uniform conditional stochastic continuity, following [50]. In conclusion, we show that uniform elliptic dynamic conductances provide an example of environments in which the so-called arbitrary starting point invariance principle may be derived from the invariance principle of a single particle starting from the origin. Therefore, our hydrodynamics result applies to the examples of quenched environments considered in, e.g., [1], [3], [6] in combination with the hypothesis of uniform ellipticity.

Original languageEnglish
Article number138
Pages (from-to)1-47
Number of pages47
JournalElectronic Journal of Probability
Volume25
DOIs
Publication statusPublished - 2020

Keywords

  • Arbitrary starting point invariance principle
  • Dynamic random conduc-tances
  • Hydrodynamic limit
  • Symmetric simple exclusion process
  • Tightness criterion

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