## Tohoku Mathematical Journal

### Products of random walks on finite groups with moderate growth

#### 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.

#### Article information

Source
Tohoku Math. J. (2), Volume 71, Number 2 (2019), 281-302.

Dates
First available in Project Euclid: 21 June 2019

https://projecteuclid.org/euclid.tmj/1561082599

Digital Object Identifier
doi:10.2748/tmj/1561082599

Mathematical Reviews number (MathSciNet)
MR3973252

Zentralblatt MATH identifier
07108040

#### Citation

Chen, Guan-Yu; Kumagai, Takashi. Products of random walks on finite groups with moderate growth. Tohoku Math. J. (2) 71 (2019), no. 2, 281--302. doi:10.2748/tmj/1561082599. https://projecteuclid.org/euclid.tmj/1561082599

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