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2020 Symmetric simple exclusion process in dynamic environment: hydrodynamics
Frank Redig, Ellen Saada, Federico Sau
Electron. J. Probab. 25: 1-47 (2020). DOI: 10.1214/20-EJP536


We consider the symmetric simple exclusion process in $\mathbb {Z}^{d}$ 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.


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Frank Redig. Ellen Saada. Federico Sau. "Symmetric simple exclusion process in dynamic environment: hydrodynamics." Electron. J. Probab. 25 1 - 47, 2020.


Received: 7 November 2018; Accepted: 21 October 2020; Published: 2020
First available in Project Euclid: 18 November 2020

MathSciNet: MR4179302
Digital Object Identifier: 10.1214/20-EJP536

Primary: 60F17 , 60J28 , 60K35 , 60K37 , 82C22

Keywords: arbitrary starting point invariance principle , dynamic random conductances , Hydrodynamic limit , symmetric simple exclusion process , tightness criterion


Vol.25 • 2020
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