COMPARING MIXING TIMES ON SPARSE RANDOM GRAPHS

Abstract : It is natural to expect that nonbacktracking random walk will mix faster than simple random walks, but so far this has only been proved in regular graphs. To analyze typical irregular graphs, let G be a random graph on n vertices with minimum degree 3 and a degree distribution that has exponential tails. We determine the precise worst-case mixing time for simple random walk on G, and show that, with high probability, it exhibits cutoff at time h −1 log n, where h is the asymptotic entropy for simple random walk on a Galton–Watson tree that approximates G locally. (Previously this was only known for typical starting points.) Furthermore, we show this asymptotic mixing time is strictly larger than the mixing time of nonbacktracking walk, via a delicate comparison of entropies on the Galton–Watson tree.
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Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01598912
Contributeur : Anna Ben-Hamou <>
Soumis le : samedi 30 septembre 2017 - 12:23:11
Dernière modification le : lundi 9 octobre 2017 - 01:08:46

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  • HAL Id : hal-01598912, version 1

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INSMI | USPC | PMA | UPMC

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Anna Ben-Hamou, Eyal Lubetzky, Yuval Peres. COMPARING MIXING TIMES ON SPARSE RANDOM GRAPHS. 2017. 〈hal-01598912〉

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