A Simple Proof of the DPRZ-Theorem for 2D Cover Times

TL;DR

This paper offers a straightforward proof of the DPRZ-Theorem, clarifying the leading order of cover times in two-dimensional settings for small epsilon, thus simplifying understanding of this fundamental result.

Contribution

It provides a concise and accessible proof of the DPRZ-Theorem, enhancing comprehension of 2D cover times without altering the original theorem.

Findings

Confirmed the leading order of 2D cover times in the small-epsilon regime

Simplified the proof of the DPRZ-Theorem

Enhanced understanding of cover time asymptotics

Abstract

The purpose of these short notes is to provide a concise proof of a celebrated theorem by Dembo, Peres, Rosen and Zeitouni, which settles the leading order of cover times in the small-\varepsilon regime.