On the distribution of the length of the second row of a young diagram under plancherel measure

Jinho Baik, Percy Deift, Kurt Johansson

Research output: Contribution to journalArticle

Abstract

We investigate the probability distribution of the length of the second row of a Young diagram of size N equipped with Plancherel measure. We obtain an expression for the generating function of the distribution in terms of a derivative of an associated Fredholm determinant, which can then be used to show that as N → ∞ the distribution converges to the Tracy-Widom distribution [TW1] for the second largest eigenvalue of a random GUE matrix. This paper is a sequel to [BDJ], where we showed that as N → ∞ the distribution of the length of the first row of a Young diagram, or equivalently, the length of the longest increasing subsequence of a random permutation, converges to the Tracy-Widom distribution [TW1] for the largest eigenvalue of a random GUE matrix.

Original languageEnglish (US)
Pages (from-to)702-731
Number of pages30
JournalGeometric and Functional Analysis
Volume10
Issue number4
DOIs
StatePublished - 2000

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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