Symmetric simple exclusion process in dynamic environment: hydrodynamics
arXiv:1811.01366 · doi:10.1214/20-ejp536
Abstract
We consider the symmetric simple exclusion process in 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 \cite{nagy_symmetric_2002}, 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 \cite{varadhan_stochasticprocesses_2007}. 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.,\ \cite{andres2014}, \cite{andres_quenched_2018}, \cite{biskup_invariance_2019} in combination with the hypothesis of uniform ellipticity.
References in corpus (8)
- Duality for stochastic models of transport
- Random walks in dynamic random environments: A transference principle
- Quenched invariance principle for random walks with time-dependent ergodic degenerate weights
- Limit theory for random walks in degenerate time-dependent random environments
- Quenched invariance principles for random walks and elliptic diffusions in random media with boundary
- Invariance Principle for the Random Conductance Model with dynamic bounded Conductances
- Scaling limits for gradient systems in random environment
- An invariance principle for one-dimensional random walks among dynamical random conductances