Large deviations for the exclusion process with a slow bond

TL;DR

This paper establishes large deviations estimates for a symmetric exclusion process with a slow bond, revealing how the slow bond influences the hydrodynamic behavior and boundary conditions in the continuum limit.

Contribution

It provides the first large deviations analysis for the exclusion process with a slow bond, accounting for Robin boundary conditions in the continuum.

Findings

Large deviations estimates derived for the process

Identification of Robin boundary conditions in the continuum limit

Extension of hydrodynamic limit results to large deviations regime

Abstract

We consider the one-dimensional symmetric simple exclusion process with a slow bond. In this model, whilst all the transition rates are equal to one, a particular bond, the \emph{slow bond}, has associated transition rate of value $N^{-1}$, where $N$ is the scaling parameter. This model has been considered in previous works on the subject of hydrodynamic limit and fluctuations. In this paper, assuming uniqueness for weak solutions of hydrodynamic equation associated to the perturbed process, we obtain dynamical large deviations estimates in the diffusive scaling. The main challenge here is the fact that the presence of the slow bond gives rise to Robin's boundary conditions in the \emph{continuum}, substantially complicating the large deviations scenario.