## 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 language | English (US) |
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Pages (from-to) | 702-731 |

Number of pages | 30 |

Journal | Geometric and Functional Analysis |

Volume | 10 |

Issue number | 4 |

DOIs | |

State | Published - 2000 |

## ASJC Scopus subject areas

- Analysis
- Geometry and Topology