Tohoku Mathematical Journal
2019
June
SECOND SERIES VOL. 71, NO. 2

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

Title PRODUCTS OF RANDOM WALKS ON FINITE GROUPS WITH MODERATE GROWTH

Author Guan-Yu Chen and Takashi Kumagai

(Received March 21, 2017, revised May 1, 2017)
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.

Mathematics Subject Classification. Primary 60J10; Secondary 60J27.
Key words and phrases. Product chains, random walks, moderate growth.

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