Large deviations for stable like random walks on $\mathbb Z^d$ with applications to random walks on wreath products

TL;DR

This paper establishes large deviation principles for occupation times of stable-like random walks on integer lattices and applies these results to analyze random walks on wreath products, revealing new asymptotic behaviors.

Contribution

It introduces Donsker-Varadhan type large deviation results for occupation times of stable-like walks and applies them to wreath product groups, extending classical results to new settings.

Findings

Derived large deviation principles for occupation times of stable-like walks.

Applied these principles to analyze random walks on wreath products.

Provided asymptotic estimates for occupation times in complex group structures.

Abstract

We derive Donsker-Vardhan type results for functionals of the occupation times when the underlying random walk on $\mathbb Z^d$ is in the domain of attraction of an operator-stable law on $\mathbb R^d$. Applications to random walks on wreath products (also known as lamplighter groups) are given.