Bounded cutoff window for the non-backtracking random walk on Ramanujan Graphs

TL;DR

This paper proves that non-backtracking random walks on Ramanujan graphs with large girth achieve the fastest possible mixing time cutoff within a bounded window, advancing understanding of random walk behavior on special graphs.

Contribution

It establishes the precise cutoff phenomenon for non-backtracking random walks on Ramanujan graphs with large girth, showing optimal mixing speed.

Findings

Non-backtracking random walk exhibits cutoff on Ramanujan graphs.

Cutoff occurs within a bounded window, indicating rapid mixing.

Results are optimal for this class of graphs.

Abstract

We prove that the non-backtracking random walk on Ramanujan graphs with large girth exhibits the fastest possible cutoff with a bounded window.