On the asymptotic behaviour of convolution powers of probabilities on discrete groups
type: Item
instance of: scholarly article
title: On the asymptotic behaviour of convolution powers of probabilities on discrete groups
zbMATH Open document ID: 0663.43001
DOI: 10.1007/BF01517356
author: Donald I. Cartwright
published in: Monatshefte für Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178428
review text: It is shown that there is a discrete countable group \(\Gamma\) and two finitely-supported symmetric probabilities \(\mu_ 1\) and \(\mu_ 2\) on \(\Gamma\) so that both \(Supp(\mu_ 1)\) and \(Supp(\mu_ 2)\) generate \(\Gamma\) and so that \(\mu_ 1^{*n}(e)\sim C_ 1\sigma^ n_ 1/n^{\alpha_ 1}\) and \(\mu_ 2^{*n}(e)\sim C_ 2\sigma^ n_ 2/n^{\alpha_ 2}\) as \(n\to \infty\), where \(0<\sigma_ 1,\sigma_ 2<1\), \(C_ 1,C_ 2>0\) and \(\alpha_ 1,\alpha_ 2>0\), with \(\alpha_ 1\neq \alpha_ 2\). This settles a conjecture of P. Gerl.
Mathematics Subject Classification ID: 43A05
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 4084293
zbMATH Keywords: local limit theorems
zbMATH Keywords: convolution powers
zbMATH Keywords: finitely-supported symmetric probabilities
MaRDI profile type: Publication
cites work: Some examples of random walks on free products of discrete groups
cites work: Q3029939
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OpenAlex ID: W2052501592
description: scientific article; zbMATH DE number 4084293