Rate of escape of random walks on wreath products and related groups.
type: Item
instance of: scholarly article
title: Rate of escape of random walks on wreath products and related groups.
zbMATH Open document ID: 1051.60047
author: David Revelle
published in: The Annals of Probability
publication date: 2004-07-01T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.aop/1068646371
review text: The author proves analogues of the law of the iterated logarithm for random walks on wreath products and related groups. For groups of polynomial growth, such results can be found in [\textit{W. Hebisch} and \textit{L. Saloff-Coste}, Ann. Probab. 21, No. 2, 673--709 (1993; Zbl 0776.60086)], for those with exponential growth and linear escape rate see \textit{A. M. Vershik} [Russ. Math. Surv. 55, No. 4, 667--733 (2000); translation from Usp. Mat. Nauk 55, No. 4, 59--128 (2000; Zbl 0991.37005)]. Here, the groups studied have exponential growth but sublinear escape rate. Concrete examples studied include Lamplighter groups, Baumslag-Solitar groups and a discrete version of the Sol geometry.
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60B15
zbMATH DE Number: 2077581
reviewed by: A. D. Barbour
MaRDI profile type: Publication
OpenAlex ID: W1994720697
cites work: A Lower Estimate for Central Probabilities on Polycyclic Groups
cites work: Q4043899
cites work: Strong invariance for local times
cites work: Large deviations for random walks on Galton-Watson trees: Averaging and uncertainty
cites work: Q3891523
cites work: Q5807214
cites work: Escape rate of brownian motion on riemanian manifolds
cites work: Gaussian estimates for Markov chains and random walks on groups
cites work: Random walks on discrete groups: Boundary and entropy
cites work: An iterated logarithm law for local time
cites work: Random walks on the lamplighter group
cites work: On random walks on wreath products
cites work: Biased random walk on lamplighter groups and graphs
cites work: Q3998747
cites work: Random walks on wreath products of groups
cites work: Q3314638
cites work: Q3336429
cites work: Q3706274
cites work: Q3315713
cites work: Dynamic theory of growth in groups: Entropy, boundaries, examples
DOI: 10.1214/AOP/1068646371
description: scientific article; zbMATH DE number 2077581