Mixing Rates of Random Walks with Little Backtracking

TL;DR

This paper investigates the mixing rates of specific random walks on regular graphs with a clique partition structure, generalizing previous results on non-backtracking walks to broader classes of graphs.

Contribution

It introduces a generalized analysis of mixing rates for random walks on graphs with clique partitions, extending prior work on non-backtracking walks.

Findings

Derived new bounds for mixing rates on clique-partitioned graphs

Extended non-backtracking walk results to more general graph structures

Provided theoretical insights into random walk behavior on regular graphs

Abstract

Many regular graphs admit a natural partition of their edge set into cliques of the same order such that each vertex is contained in the same number of cliques. In this paper, we study the mixing rate of certain random walks on such graphs and we generalize previous results of Alon, Benjamini, Lubetzky and Sodin regarding the mixing rates of non-backtracking random walks on regular graphs.