Comparing mixing times on sparse random graphs

Anna Ben-Hamou, Eyal Lubetzky, Yuval Peres

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1116-1130
Number of pages15
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume55
Issue number2
DOIs
StatePublished - May 1 2019

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Mixing Time
Simple Random Walk
Sparse Graphs
Random Graphs
Entropy
Degree Distribution
Minimum Degree
Regular Graph
Walk
Irregular
Tail
Random walk
Strictly
Graph in graph theory
Random graphs
Graph

Keywords

  • Mixing times of Markov chains
  • Nonbacktracking vs. Simple random walk
  • Random graphs
  • Random walks

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Comparing mixing times on sparse random graphs. / Ben-Hamou, Anna; Lubetzky, Eyal; Peres, Yuval.

In: Annales de l'institut Henri Poincare (B) Probability and Statistics, Vol. 55, No. 2, 01.05.2019, p. 1116-1130.

Research output: Contribution to journalArticle

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