Mixing time bounds for edge flipping on regular graphs

TL;DR

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

Contribution

It provides new lower bounds for convergence rates on regular graphs and proves a cutoff at 1/4 n log n for complete graphs using coupling methods.

Findings

Lower bound for convergence rate on regular graphs

Cutoff at 1/4 n log n for complete graph edge flipping

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 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 1/4 n log n for the edge flipping on the complete graph by a coupling argument