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2019 Products of random walks on finite groups with moderate growth
Guan-Yu Chen, Takashi Kumagai
Tohoku Math. J. (2) 71(2): 281-302 (2019). DOI: 10.2748/tmj/1561082599

Abstract

In this article, we consider products of random walks on finite groups with moderate growth and discuss their cutoffs in the total variation. Based on several comparison techniques, we are able to identify the total variation cutoff of discrete time lazy random walks with the Hellinger distance cutoff of continuous time random walks. Along with the cutoff criterion for Laplace transforms, we derive a series of equivalent conditions on the existence of cutoffs, including the existence of pre-cutoffs, Peres' product condition and a formula generated by the graph diameters. For illustration, we consider products of Heisenberg groups and randomized products of finite cycles.

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Guan-Yu Chen. Takashi Kumagai. "Products of random walks on finite groups with moderate growth." Tohoku Math. J. (2) 71 (2) 281 - 302, 2019. https://doi.org/10.2748/tmj/1561082599

Information

Published: 2019
First available in Project Euclid: 21 June 2019

zbMATH: 07108040
MathSciNet: MR3973252
Digital Object Identifier: 10.2748/tmj/1561082599

Subjects:
Primary: 60J10
Secondary: 60J27

Rights: Copyright © 2019 Tohoku University

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Vol.71 • No. 2 • 2019
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