# Large deviations of the range of the planar random walk on the scale of the mean

## TL;DR

This paper establishes an upper large deviation bound for the range of a symmetric planar random walk with finite sixth moment, complementing existing studies on Wiener Sausages and higher dimensions.

## Contribution

It provides a new large deviation bound for planar random walks, extending the understanding of their behavior on the scale of the mean.

## Key findings

- Upper large deviation bound established
- Complements previous Wiener Sausage studies
- Focuses on planar random walk with finite sixth moment

## Abstract

We show an upper large deviation bound on the scale of the mean for a symmetric random walk in the plane with finite sixth moment. This result complements the study of Van den Berg, Bolthausen and Den Hollander, where the continuum case of the Wiener Sausage is studied, and in Phetpradap, in which one is restricted to dimension three and higher.