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Random walks on free products, quotients and amalgams

Published online by Cambridge University Press:  22 January 2016

Donald I. Cartwright  and
P. M. Soardi
Donald I. Cartwright
Affiliation:
Department of Pure Mathematics, The University of Sydney, Sydney N.S.W. 2006, Australia
P. M. Soardi
Affiliation:
Dipartimento di Matematica, Università di Milano, Via C. Saldini 50, Milano, 20133, Italy
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Suppose that G is a discrete group and p is a probability measure on G. Consider the associated random walk {Xn} on G. That is, let Xn = Y1Y2 … Yn, where the Yj’s are independent and identically distributed G-valued variables with density p. An important problem in the study of this random walk is the evaluation of the resolvent (or Green’s function) R(z, x) of p. For example, the resolvent provides, in principle, the values of the n step transition probabilities of the process, and in several cases knowledge of R(z, x) permits a description of the asymptotic behaviour of these probabilities.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 102 , June 1986 , pp. 163 - 180
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1986

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