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Asymptotics of q-plancherel measures
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  • Published: 01 December 2010

Asymptotics of q-plancherel measures

  • Valentin Féray1 &
  • Pierre-Loïc Méliot2 

Probability Theory and Related Fields volume 152, pages 589–624 (2012)Cite this article

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Abstract

In this paper, we are interested in the asymptotic size of the rows and columns of a random Young diagram under a natural deformation of the Plancherel measure coming from Hecke algebras. The first lines of such diagrams are typically of order n, so it does not fit in the context of the work of Biane (Int Math Res Notices 4:179–192, 2001) and Śniady (Probab. Theory Relat Fields 136:263–297, 2006). Using the theory of polynomial functions on Young diagrams of Kerov and Olshanski, we are able to compute explicitly the first- and second-order asymptotics of the length of the first rows. Our method also works for other measures, for example those coming from Schur–Weyl representations.

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Author information

Authors and Affiliations

  1. Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université Bordeaux 1, 351 cours de la Libération, 33400, Talence, France

    Valentin Féray

  2. The Gaspard–Monge Institut of Electronique and Computer Science, University of Marne-La-Vallée Paris-Est, 77454, Marne-la-Vallée Cedex 2, France

    Pierre-Loïc Méliot

Authors
  1. Valentin Féray
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  2. Pierre-Loïc Méliot
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Correspondence to Valentin Féray.

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Féray, V., Méliot, PL. Asymptotics of q-plancherel measures. Probab. Theory Relat. Fields 152, 589–624 (2012). https://doi.org/10.1007/s00440-010-0331-6

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  • Received: 25 January 2010

  • Revised: 11 October 2010

  • Published: 01 December 2010

  • Issue Date: April 2012

  • DOI: https://doi.org/10.1007/s00440-010-0331-6

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Keywords

  • Asymptotics of Young diagrams
  • Hecke algebras
  • Deformation of Plancherel measure

Mathematics Subject Classification (2000)

  • 60C05
  • 20C30
  • 20C08
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