Permutation model for semi-circular systems and quantum random walks
type: Item
instance of: scholarly article
title: Permutation model for semi-circular systems and quantum random walks
zbMATH Open document ID: 0854.60070
published in: Pacific Journal of Mathematics
publication date: 1996-07-31T00:00:00Z
review text: Let \(E\) be a countable set with a fixed element \(e_0\), \(S(E)\) the group of permutations with finite support of \(E\) and \((e^j_n)_{n \in \mathbb{N}}\) for \(j \in J\) be disjoint sequences in \(E\). Let \(\tau^j_n\) be the transposition \((e_0, e^j_n)\), it is proved that the family of noncommutative random variables \((a^j_N = {1 \over \sqrt N} \sum^N_{n = 1} \tau^j_n\), \(j \in J) \) in the group-von Neumann algebra of \(S(E)\) converges in distribution towards a semicircular system. By using some results on random walks on the dual of unitary groups a relation between this result and the random matrix model for semicircular systems of Voiculescu is exhibited.
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 912150
zbMATH Keywords: permutations
zbMATH Keywords: random walks
zbMATH Keywords: semi-circular systems
author: Philippe Biane
reviewed by: Philippe Biane
MaRDI profile type: Publication
full work available at URL: pjm.1995.171.373
OpenAlex ID: W1860719571
DOI: 10.2140/PJM.1995.171.373
description: scientific article; zbMATH DE number 912150