Cover times and generic chaining

TL;DR

This paper simplifies the proof of a recent result relating the cover time of random walks on graphs to generic chaining, using elementary hitting time estimates and chaining arguments, though it does not fully recover the original result.

Contribution

It provides a simpler, more elementary approach to bounding cover times via generic chaining, improving understanding and accessibility of the original complex proof.

Findings

Simpler proof of the connection between cover times and generic chaining.

Partial recovery of Ding, Lee, and Peres's original result.

Method based on elementary hitting time estimates and chaining arguments.

Abstract

A recent result of Ding, Lee and Peres expresses the cover time of the random walk on a graph in terms of generic chaining for the commute distance. Their proof is very involved and the purpose of this article is to present a simpler approach to this problem based on elementary hitting times estimates and chaining arguments. Unfortunately we fail to recover their full result, but not by much.