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Mixing time bounds for edge flipping on regular graphs

Part of: Limit theorems Stochastic processes Combinatorial probability

Published online by Cambridge University Press:  26 April 2023

Yunus Emre Demirci ,
Ümit Işlak  and
Alperen Özdemir Open the ORCID record for Alperen Özdemir [Opens in a new window]
Yunus Emre Demirci*
Affiliation:
Queen’s University
Ümit Işlak*
Affiliation:
Boğaziçi University
Alperen Özdemir*
Affiliation:
Georgia Institute of Technology
*
*Postal address: Queen’s University, Department of Mathematics and Statistics, Kingston, Ontario, Canada. Email: 21yed@queensu.ca
**Postal address: Boğaziçi University, Department of Mathematics, Istanbul, Turkey. Email: umit.islak1@boun.edu.tr
***Postal address: Georgia Institute of Technology, School of Mathematics, Atlanta, GA, USA. Email: aozdemir6@gatech.edu
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Abstract

An edge flipping is a non-reversible Markov chain on a given connected graph, as defined in Chung and Graham (2012). In the same paper, edge flipping eigenvalues and stationary distributions for some classes of graphs were identified. We further study edge flipping spectral properties to show a lower bound for the rate of convergence in the case of regular graphs. Moreover, we show by a coupling argument that a cutoff occurs at $\frac{1}{4} n \log n$ for the edge flipping on the complete graph.

Keywords

Couplingedge flippinghyperplane arrangementsMarkov chainsregular graphs

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 60F05: Central limit and other weak theorems 60G42: Martingales with discrete parameter
Type
Original Article
Information
Journal of Applied Probability , Volume 60 , Issue 4 , December 2023 , pp. 1317 - 1332
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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