Comparing mixing times on sparse random graphs

Anna Ben-Hamou, Eyal Lubetzky, Yuval Peres

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 cutof 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)
Title of host publication29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
PublisherAssociation for Computing Machinery
Pages1734-1740
Number of pages7
ISBN (Electronic)9781611975031
DOIs
StatePublished - Jan 1 2018
Event29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 - New Orleans, United States
Duration: Jan 7 2018Jan 10 2018

Other

Other29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
CountryUnited States
CityNew Orleans
Period1/7/181/10/18

Fingerprint

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

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

Cite this

Ben-Hamou, A., Lubetzky, E., & Peres, Y. (2018). Comparing mixing times on sparse random graphs. In 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 (pp. 1734-1740). Association for Computing Machinery. https://doi.org/10.1137/1.9781611975031.113

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

29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018. Association for Computing Machinery, 2018. p. 1734-1740.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ben-Hamou, A, Lubetzky, E & Peres, Y 2018, Comparing mixing times on sparse random graphs. in 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018. Association for Computing Machinery, pp. 1734-1740, 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018, New Orleans, United States, 1/7/18. https://doi.org/10.1137/1.9781611975031.113
Ben-Hamou A, Lubetzky E, Peres Y. Comparing mixing times on sparse random graphs. In 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018. Association for Computing Machinery. 2018. p. 1734-1740 https://doi.org/10.1137/1.9781611975031.113
Ben-Hamou, Anna ; Lubetzky, Eyal ; Peres, Yuval. / Comparing mixing times on sparse random graphs. 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018. Association for Computing Machinery, 2018. pp. 1734-1740
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