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Journal of Theoretical Probability

, Volume 32, Issue 2, pp 684–701 | Cite as

Improved Mixing Rates of Directed Cycles by Added Connection

  • Balázs GerencsérEmail author
  • Julien M. Hendrickx
Article
  • 20 Downloads

Abstract

We investigate the mixing rate of a Markov chain where a combination of long distance edges and non-reversibility is introduced. As a first step, we focus here on the following graphs: starting from the cycle graph, we select random nodes and add all edges connecting them. We prove a square-factor improvement of the mixing rate compared to the reversible version of the Markov chain.

Keywords

Mixing rate Random graphs Non-reversibility 

Mathematics Subject Classification (2010)

60J10 05C80 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.MTA Alfréd Rényi Institute of MathematicsBudapestHungary
  2. 2.ICTEAM InstituteUniversité catholique de LouvainLouvain-la-NeuveBelgium

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