Cutoff for random lifts of weighted graphs

Abstract : We prove a cutoff for the random walk on random n-lifts of finite weighted graphs, even when the random walk on the base graph G of the lift is not reversible. The mixing time is w.h.p. t mix = h −1 log n, where h is a constant associated to G, namely the entropy of its universal cover. Moreover, this mixing time is the smallest possible among all n-lifts of G. In the particular case where the base graph is a vertex with d/2 loops, d even, we obtain a cutoff for a d-regular random graph (as did Lubetzky and Sly in [26] with a slightly different distribution on d-regular graphs, but the mixing time is the same).
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https://hal.archives-ouvertes.fr/hal-02265116
Contributor : Guillaume Conchon--Kerjan <>
Submitted on : Thursday, August 8, 2019 - 2:30:26 PM
Last modification on : Sunday, August 11, 2019 - 1:08:31 AM

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Guillaume Conchon--Kerjan. Cutoff for random lifts of weighted graphs. 2019. ⟨hal-02265116⟩

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