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Distribution of the shape of Markovian random words
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  • Published: 02 February 2004

Distribution of the shape of Markovian random words

  • G.P. Chistyakov1 &
  • F. Götze2 

Probability Theory and Related Fields volume 129, pages 18–36 (2004)Cite this article

  • 67 Accesses

  • 4 Citations

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Abstract.

The distribution of the shape λ of the semi-standard tableau of a random word in k letters is asymptotically given by the distribution of the spectrum of a random traceless k×k Gaussian Unitary Ensemble (GUE) matrix provided that these letters are independent with uniform distribution. Kuperberg (2002) conjectured that this result by Johansson (2001) remains valid if the letters of the word are generated by an irreducible Markov chain on the alphabet with cyclic transition matrix. In this paper we give a proof of this conjecture for an alphabet with k=2 letters.

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Author information

Authors and Affiliations

  1. Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., 61103, Kharkov, Ukraine

    G.P. Chistyakov

  2. Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501, Bielefeld 1, Germany

    F. Götze

Authors
  1. G.P. Chistyakov
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  2. F. Götze
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Corresponding author

Correspondence to G.P. Chistyakov.

Additional information

Research supported by DFG GO-420/3-3 in Bielefeld.

Research supported by INTAS 99-00317, RFBR–DFG 99-01-04027.

Mathematics Subject Classification (2000): 82B41, 60C05, 60F05, 60F10

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Cite this article

Chistyakov, G., Götze, F. Distribution of the shape of Markovian random words. Probab. Theory Relat. Fields 129, 18–36 (2004). https://doi.org/10.1007/s00440-003-0327-6

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  • Received: 05 June 2003

  • Revised: 10 November 2003

  • Published: 02 February 2004

  • Issue Date: May 2004

  • DOI: https://doi.org/10.1007/s00440-003-0327-6

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Key words or phrases

  • Random words
  • central limits
  • random matrices
  • Markov’s chain
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