Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [15 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01598912
Contributor : Anna Ben-Hamou <>
Submitted on : Saturday, September 30, 2017 - 12:23:11 PM
Last modification on : Friday, March 27, 2020 - 3:50:35 AM
Document(s) archivé(s) le : Sunday, December 31, 2017 - 12:50:21 PM

File

comparing-mixing.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01598912, version 1

Citation

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

Share

Metrics

Record views

332

Files downloads

323