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)|
|Number of pages||30|
|Journal||Geometric and Functional Analysis|
|State||Published - 2000|
ASJC Scopus subject areas
- Geometry and Topology