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

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

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.

Suggested Citation

  • Avena, Luca & Güldaş, Hakan & van der Hofstad, Remco & den Hollander, Frank & Nagy, Oliver, 2022. "Linking the mixing times of random walks on static and dynamic random graphs," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 145-182.
    • Handle: RePEc:eee:spapps:v:153:y:2022:i:c:p:145-182
    DOI: 10.1016/j.spa.2022.07.009
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    1. Avena, Luca & Güldaş, Hakan & Hofstad, Remco van der & Hollander, Frank den, 2019. "Random walks on dynamic configuration models:A trichotomy," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3360-3375.
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