Quenched large deviations in renewal theory

TL;DR

This paper develops quenched large deviation principles for renewal-reward processes in random environments with rewards in Banach spaces, providing variational formulas and illustrating with three complex examples.

Contribution

It introduces quenched large deviation principles for renewal-reward processes in random environments, including variational formulas involving correctors, and applies to diverse models.

Findings

Established quenched large deviation principles for complex renewal processes.

Derived explicit variational formulas for rate functions.

Demonstrated applications to polymers, compound Poisson processes, and Markov chains.

Abstract

In this paper we introduce and study renewal-reward processes in random environments where each renewal involves a reward taking values in a Banach space. We derive quenched large deviation principles and identify the associated rate functions in terms of variational formulas involving correctors. We illustrate the theory with three examples: compound Poisson processes in random environments, pinning of polymers at interfaces with disorder, and returns of Markov chains in dynamic random environments.