A note on the intersections of two random walks in two dimensions

TL;DR

This paper establishes a large deviation principle for the intersection of two independent two-dimensional random walks, extending previous work focused on higher dimensions.

Contribution

It provides the first large deviation result specifically for the intersection behavior of two-dimensional random walks.

Findings

Proves a large deviation principle for intersection ranges in 2D.

Complements existing results for higher dimensions.

Enhances understanding of intersection probabilities in low-dimensional random walks.

Abstract

In this note we prove a large deviation result for the intersection of the ranges of two independent random walks in dimension two. This complements the study of Phetpradap from 2011, where the intersection in dimension three and above was studied.