The cut-off phenomenon for random reflections. II: Complex and quaternionic cases
type: Item
instance of: scholarly article
title: The cut-off phenomenon for random reflections. II: Complex and quaternionic cases
zbMATH Open document ID: 0865.60005
DOI: 10.1007/BF01247837
publication date: 1997-07-07T00:00:00Z
review text: We generalize the random reflections problem on \(O(N)\) considered in part I [Ann. Probab. 24, No. 1, 74-96 (1996; Zbl 0854.60068)] to the complex and quaternionic cases. We give precise estimates on the speed of convergence to stationarity for specific examples of random walks on \(U(N)\) and \(Sp(N)\) for which the one-step distribution is a certain probability measure concentrated on reflections. Our results show that in both cases the so-called cut-off phenomenon occurs at \(k_0={1\over 2} N\log N\).
Mathematics Subject Classification ID: 60B15
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 849093
zbMATH Keywords: random reflections problem
zbMATH Keywords: speed of convergence
zbMATH Keywords: cut-off phenomenon
author: Ursula Porod
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 849093