The resolvent for simple random walks on the free product of two discrete groups
type: Item
instance of: scholarly article
title: The resolvent for simple random walks on the free product of two discrete groups
zbMATH Open document ID: 0608.60015
DOI: 10.1007/BF01162024
author: Paolo M. Soardi
published in: Mathematische Zeitschrift
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173719
review text: The author studies symmetric random walks on the free product \(G=G_ 1*G_ 2\) of two discrete groups; such a random walk is given by a probability \(p=a_ 1p_ 1+a_ 2p_ 2\), where \(p_ i\) are symmetric probabilities on \(G_ i\), \(p_ i(e)=0\) and \(a_ 1+a_ 2=1\). The author gives a method using Stieltjes transforms to calculate the resolvent \((=power\) series in \(z^{-1}\) with coefficients \(p^{*n}(e))\) of p from the resolvents of \(p_ i\). In some particular cases he gets from this local limit theorems. Similar results using another method were obtained by \textit{W. Woess}, Random walks on free products of discrete groups. Boll. Unione Mat. Ital. (1987).
Mathematics Subject Classification ID: 60B15
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 3984203
zbMATH Keywords: Stieltjes transforms
zbMATH Keywords: local limit theorems
zbMATH Keywords: free products of discrete groups
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3984203