Hitting times of rare events in boundary driven symmetric simple exclusion processes

TL;DR

This paper studies the hitting times of rare events in a boundary-driven symmetric simple exclusion process, showing that the first visit time to certain density profiles follows an exponential distribution.

Contribution

It proves the convergence of hitting times to an exponential distribution for non-stationary density profiles in the process.

Findings

Hitting times converge to exponential distribution

Results apply to open sets of density profiles not containing the stationary profile

Provides insight into the timing of rare events in exclusion processes

Abstract

In the boundary driven symmetric simple exclusion process consider an open set $\ms O$ of density profiles which does not contain the stationary density profile. We prove that the first time the empirical measure visits the set $\ms O$ converges to an exponential distribution.