Long-time behavior of SSEP with slow boundary

TL;DR

This paper studies the long-term behavior of the symmetric simple exclusion process with slow boundary conditions, proving a law of large numbers for the empirical measure under extended time scaling.

Contribution

It introduces a longer time scaling analysis for the SSEP with slow boundary, extending previous diffusive time scale results.

Findings

Law of large numbers for empirical measure under extended time scale

Extension of previous diffusive scaling results

Insights into boundary effects on long-term behavior

Abstract

We consider the symmetric simple exclusion process with slow boundary first introduced in [Baldasso {\it et al.}, Journal of Statistical Physics, 167(5), 2017]. We prove a law of large number for the empirical measure of the process under a longer time scaling instead of the usual diffusive time scaling.