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May 2017 Cutoff for nonbacktracking random walks on sparse random graphs
Anna Ben-Hamou, Justin Salez
Ann. Probab. 45(3): 1752-1770 (May 2017). DOI: 10.1214/16-AOP1100

Abstract

A finite ergodic Markov chain exhibits cutoff if its distance to stationarity remains close to 1 over a certain number of iterations and then abruptly drops to near 0 on a much shorter time scale. Discovered in the context of card shuffling (Aldous–Diaconis, 1986), this phenomenon is now believed to be rather typical among fast mixing Markov chains. Yet, establishing it rigorously often requires a challengingly detailed understanding of the underlying chain. Here, we consider nonbacktracking random walks on random graphs with a given degree sequence. Under a general sparsity condition, we establish the cutoff phenomenon, determine its precise window and prove that the cutoff profile approaches a remarkably simple, universal shape.

Citation

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Anna Ben-Hamou. Justin Salez. "Cutoff for nonbacktracking random walks on sparse random graphs." Ann. Probab. 45 (3) 1752 - 1770, May 2017. https://doi.org/10.1214/16-AOP1100

Information

Received: 1 April 2015; Revised: 1 January 2016; Published: May 2017
First available in Project Euclid: 15 May 2017

zbMATH: 1372.60101
MathSciNet: MR3650414
Digital Object Identifier: 10.1214/16-AOP1100

Subjects:
Primary: 05C80, 05C81, 60G50, 60J10

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 3 • May 2017
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