A Fredholm determinant identity and the convergence of moments for random young tableaux

Jinho Baik, Percy Deift, Eric Rains

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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.

Original languageEnglish (US)
Pages (from-to)627-672
Number of pages46
JournalCommunications In Mathematical Physics
Volume223
Issue number3
DOIs
StatePublished - Nov 1 2001

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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