TY - GEN

T1 - Comparing mixing times on sparse random graphs

AU - Ben-Hamou, Anna

AU - Lubetzky, Eyal

AU - Peres, Yuval

N1 - Publisher Copyright:
© Copyright 2018 by SIAM.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85045572944&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85045572944&partnerID=8YFLogxK

U2 - 10.1137/1.9781611975031.113

DO - 10.1137/1.9781611975031.113

M3 - Conference contribution

AN - SCOPUS:85045572944

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1734

EP - 1740

BT - 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018

A2 - Czumaj, Artur

PB - Association for Computing Machinery

T2 - 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018

Y2 - 7 January 2018 through 10 January 2018

ER -