Mixing time bounds for edge flipping on regular graphs

TL;DR

This paper analyzes the spectral properties of the edge flipping Markov chain on regular graphs, establishing convergence bounds and demonstrating a cutoff phenomenon on the complete graph.

Contribution

It provides new lower bounds for convergence rates on regular graphs and proves a cutoff at rac{1}{4} n ext{log} n for the complete graph using coupling methods.

Findings

Lower bound for convergence rate on regular graphs

Cutoff phenomenon at rac{1}{4} n ext{log} n on complete graph

Spectral analysis of edge flipping Markov chain

Abstract

The edge flipping is a non-reversible Markov chain on a given connected graph, which is defined by Chung and Graham in [CG12]. In the same paper, its eigenvalues and stationary distributions for some classes of graphs are identified. We further study its spectral properties to show a lower bound for the rate of convergence in the case of regular graphs. Moreover, we show that a cutoff occurs at \frac{1}{4} n \log n for the edge flipping on the complete graph by a coupling argument.