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Communications in Mathematical Physics

, Volume 223, Issue 3, pp 627–672 | Cite as

A Fredholm Determinant Identity and the Convergence of Moments for Random Young Tableaux

  • Jinho Baik
  • Percy Deift
  • Eric Rains

Abstract:

We obtain an identity between Fredholm determinants of two kinds of operators, one acting on functions on the unit circle and the other acting on functions on a subset of the integers. This identity is a generalization of an identity between a Toeplitz determinant and a Fredholm determinant that has appeared in the random permutation context. Using this identity, we prove, in particular, convergence of moments for arbitrary rows of a random Young diagram under Plancherel measure.

Keywords

Unit Circle Young Diagram Random Permutation Young Tableau Fredholm Determinant 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Jinho Baik
    • 1
  • Percy Deift
    • 2
  • Eric Rains
    • 3
  1. 1.Department of Mathematics, Princeton University, Princeton, NJ 08544, USA.¶E-mail: jbaik@math.princeton.eduUS
  2. 2.Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104, USA.¶E-mail: deift@math.upenn.eduUS
  3. 3.AT&T Research, Florham Park, NJ 07932, USA.¶E-mail: rains@research.att.comUS

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