Large deviations and path properties of the true self-repelling motion

TL;DR

This paper establishes large deviation bounds for the true self-repelling motion, a self-interacting process, and analyzes its path properties, including laws of iterated logarithms, highlighting its distinct behavior from standard diffusions.

Contribution

It provides the first large deviation bounds and detailed path property analysis for the true self-repelling motion, a novel self-interacting stochastic process.

Findings

Derived large deviation bounds for the process

Analyzed law of iterated logarithms for small and large times

Showed the process has markedly different path properties from diffusions

Abstract

We derive some large deviation bounds for events related to the "true self-repelling motion", a one-dimensional self-interacting process introduced by Toth and Werner, that has very different path properties than usual diffusion processes. We then use these estimates to study certain of these path properties such as its law of iterated logarithms for both small and large times.