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Stochastic aspects of easy quantum groups
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  • Open Access
  • Published: 04 February 2010

Stochastic aspects of easy quantum groups

  • Teodor Banica1,
  • Stephen Curran2 &
  • Roland Speicher3 

Probability Theory and Related Fields volume 149, pages 435–462 (2011)Cite this article

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Abstract

We consider several orthogonal quantum groups satisfying the “easiness” assumption axiomatized in our previous paper. For each of them we discuss the computation of the asymptotic law of Tr(u k) with respect to the Haar measure, u being the fundamental representation. For the classical groups O n , S n we recover in this way some well-known results of Diaconis and Shahshahani.

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Acknowledgements

The work of T.B. was supported by the ANR grants “Galoisint” and “Granma”, and the work of R.S. was supported by a Discovery grant from NSERC.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Author information

Authors and Affiliations

  1. Department of Mathematics, Cergy-Pontoise University, 2 Avenue Chauvin, 95302, Cergy-Pontoise, France

    Teodor Banica

  2. Department of Mathematics, University of California, Berkeley, CA, 94720, USA

    Stephen Curran

  3. Department of Mathematics and Statistics, Queen’s University, Jeffery Hall, Kingston, ON, K7L 3N6, Canada

    Roland Speicher

Authors
  1. Teodor Banica
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  2. Stephen Curran
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  3. Roland Speicher
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Corresponding author

Correspondence to Roland Speicher.

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Cite this article

Banica, T., Curran, S. & Speicher, R. Stochastic aspects of easy quantum groups. Probab. Theory Relat. Fields 149, 435–462 (2011). https://doi.org/10.1007/s00440-010-0260-4

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  • Received: 01 September 2009

  • Revised: 16 December 2009

  • Published: 04 February 2010

  • Issue Date: April 2011

  • DOI: https://doi.org/10.1007/s00440-010-0260-4

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Keywords

  • Random matrices
  • Quantum group
  • Noncrossing partition

Mathematics Subject Classification (2000)

  • 60B15
  • 16T30
  • 46L54
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