Explicit LDP for a slowed RW driven by a symmetric exclusion process

TL;DR

This paper establishes a joint large deviation principle for a random walk influenced by a symmetric exclusion process, analyzing the rate functions with advanced mathematical tools and providing explicit results for the walk component.

Contribution

It introduces a joint path large deviation principle for a RW driven by SSE, with a novel decomposition of the rate function and explicit characterization of the RW component.

Findings

Joint large deviation principle proved for the RW and SSE system.

Rate function components identified as Gaussian and Poissonian.

Explicit rate function for the random walk component provided.

Abstract

We consider a random walk (RW) driven by a simple symmetric exclusion process (SSE). Rescaling the RW and the SSE in such a way that a joint hydrodynamic limit theorem holds we prove a joint path large deviation principle. The corresponding large deviation rate function can be split into two components, the rate function of the SSE and the one of the RW given the path of the SSE. Such components have different structures (Gaussian and Poissoinian, respectively) and to overcome this difficulty we make use of the theory of Orlicz spaces. In particular, the component of the rate function corresponding to the RW is explicit.