The Annals of Probability

On random walks on wreath products

C. Pittet and L. Saloff-Coste

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Abstract

Wreath products are a type of semidirect product. They play an important role in group theory. This paper studies the basic behavior of simple random walks on such groups and shows that these walks have interesting, somewhat exotic behaviors. The crucial fact is that the probability of return to the starting point of certain walks on wreath products is closely related to some functionals of the local times of a walk taking place on a simpler factor group.

Article information

Source
Ann. Probab., Volume 30, Number 2 (2002), 948-977.

Dates
First available in Project Euclid: 7 June 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1023481013

Digital Object Identifier
doi:10.1214/aop/1023481013

Mathematical Reviews number (MathSciNet)
MR1905862

Zentralblatt MATH identifier
1021.60004

Subjects
Primary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization 60G51: Processes with independent increments; Lévy processes 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]

Keywords
random walk finitely generated groups wreath product number of visited points local time amenable group

Citation

Pittet, C.; Saloff-Coste, L. On random walks on wreath products. Ann. Probab. 30 (2002), no. 2, 948--977. doi:10.1214/aop/1023481013. https://projecteuclid.org/euclid.aop/1023481013


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