Tohoku Mathematical Journal

Products of random walks on finite groups with moderate growth

Guan-Yu Chen and Takashi Kumagai

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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

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

First available in Project Euclid: 21 June 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces

product chains random walks moderate growth


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.

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