Linking the mixing times of random walks on static and dynamic random graphs

Luca Avena, Hakan Güldaş, Remco van der Hofstad, Frank den Hollander and Oliver Nagy

Stochastic Processes and their Applications, 2022, vol. 153, issue C, 145-182

Abstract: In this paper, which is a culmination of our previous research efforts, we provide a general framework for studying mixing profiles of non-backtracking random walks on dynamic random graphs generated according to the configuration model. The quantity of interest is the scaling of the mixing time of the random walk as the number of vertices of the random graph tends to infinity. Subject to mild general conditions, we link two mixing times: one for a static version of the random graph, the other for a class of dynamic versions of the random graph in which the edges are randomly rewired but the degrees are preserved. With the help of coupling arguments we show that the link is provided by the probability that the random walk has not yet stepped along a previously rewired edge.

Keywords: Configuration model; Random rewiring; Random walk; Mixing time; Cutoff (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.07.009

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