The cut-off phenomenon for random reflections II: Complex and quaternionic cases

U. Porod*

*Corresponding author for this work

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

In this paper we generalize the random reflections problem on O(N) considered in an earlier paper 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 k0 = 1/2N log N.

Original languageEnglish (US)
Pages (from-to)181-209
Number of pages29
JournalProbability Theory and Related Fields
Volume104
Issue number2
DOIs
StatePublished - Jan 1 1996

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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