An explicit formula of hitting times for random walks on graphs

TL;DR

This paper derives an explicit formula for hitting times in random walks on graphs using spanning trees, enabling improved bounds and closed-form solutions for specific graph types.

Contribution

It introduces a novel explicit formula for hitting times based on spanning tree enumeration, advancing the theoretical understanding of random walks on graphs.

Findings

Improved bound on hitting times for general graphs

Sharp bound for hitting times between adjacent vertices

Closed-form formulas for specific graph classes

Abstract

We prove an explicit formula of hitting times in terms of enumerations of spanning trees for random walks on general connected graphs. We apply the formula to improve Lawler's bound of hitting times for general graphs, prove a sharp bound of hitting times for adjacent vertices and derive closed formulas of hitting times for some special graphs.