Large Deviations Principle for Self-Intersection Local Times for random walk in dimension d>4

TL;DR

This paper establishes a large deviations principle for self-intersection local times of symmetric random walks in dimensions greater than four, providing insights into their probabilistic behavior and applications to random sceneries.

Contribution

It introduces a large deviations framework for self-intersection local times in high-dimensional random walks, extending understanding of their probabilistic properties.

Findings

Large deviations principle derived for self-intersection local times in d>4

Moderate deviations characterized for random walk in random sceneries

Enhanced understanding of high-dimensional random walk behaviors

Abstract

We obtain a large deviations principle for the self-intersection local times for a symmetric random walk in dimension d>4. As an application, we obtain moderate deviations for random walk in random sceneries in some region of parameters.