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The out-off phenomenon for random reflections II: Complex and quaternionic cases
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  • Published: June 1996

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

  • U. Porod1 

Probability Theory and Related Fields volume 104, pages 181–209 (1996)Cite this article

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  • 11 Citations

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Summary

In this paper we generalize the random reflections problem onO(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 onU(N) andSp(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 atk 0=1/2N logN.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of California, 94720, Berkeley, CA, USA

    U. Porod

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  1. U. Porod
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Additional information

This paper is based on parts of the author's doctoral dissertation written at The Johns Hopkins University

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Cite this article

Porod, U. The out-off phenomenon for random reflections II: Complex and quaternionic cases. Probab. Th. Rel. Fields 104, 181–209 (1996). https://doi.org/10.1007/BF01247837

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  • Received: 06 February 1995

  • Accepted: 24 July 1995

  • Issue Date: June 1996

  • DOI: https://doi.org/10.1007/BF01247837

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Mathematics Subject Classification (1991)

  • 60B15
  • 60J15
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