Improved mixing rates of directed cycles by added connection

Gerencser, Balazs;Hendrickx, Julien
(2019) Journal of Theoretical Probability — Vol. 32, n° 2, p. 684-701 (2019)

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(en) 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.
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Gerencser, B., & Hendrickx, J. (2019). Improved mixing rates of directed cycles by added connection. Journal of Theoretical Probability, 32(2), 684-701. https://doi.org/10.1007/s10959-018-0861-x (Original work published 2019)