Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 71, Number 2 (2019), 281-302.
Products of random walks on finite groups with moderate growth
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.
Tohoku Math. J. (2), Volume 71, Number 2 (2019), 281-302.
First available in Project Euclid: 21 June 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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