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On the Limiting Shape of Young Diagrams Associated with Inhomogeneous Random Words

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High Dimensional Probability VI

Part of the book series: Progress in Probability ((PRPR,volume 66))

Abstract

The limiting shape of the random Young diagrams associated with an inhomogeneous random word is identified as a multidimensional Brownian functional. This functional is identical in law to the spectrum of a Gaussian random matrix. Since the length of the top row of the Young diagrams is also the length of the longest (weakly) increasing subsequence of the random word, the corresponding limiting law follows. The Poissonized word problem is also briefly studied, and the asymptotic behavior of the shape analyzed.

Mathematics Subject Classification (2010). 15B52, 60C05, 60F05, 60F17, 60G22, 05A19.

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Author information

Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia, 30332-0160, USA

    Christian Houdré

  2. Department of Mathematics, Southern Polytechnic State University, Marietta, Georgia, 30060, USA

    Hua Xu

Authors
  1. Christian Houdré
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  2. Hua Xu
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Corresponding author

Correspondence to Christian Houdré .

Editor information

Editors and Affiliations

  1. Georgia Institute of Technology, Atlanta, 30332, USA

    Christian Houdré

  2. University of Delaware, Newark, 19716, USA

    David M. Mason

  3. University of Tennessee, Knoxville, 37934, USA

    Jan Rosiński

  4. University of Washington, Seattle, 98195, USA

    Jon A. Wellner

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Houdré, C., Xu, H. (2013). On the Limiting Shape of Young Diagrams Associated with Inhomogeneous Random Words. In: Houdré, C., Mason, D., Rosiński, J., Wellner, J. (eds) High Dimensional Probability VI. Progress in Probability, vol 66. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0490-5_18

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