On the distribution of the length of the second row of a Young diagram under Plancherel measure

被引：0
|
作者：
J. Baik
P. Deift
K. Johansson
机构：
[1] Courant Institute of Mathematics,
[2] NYU,undefined
[3] 251 Mercer Street,undefined
[4] New York,undefined
[5] NY 10012,undefined
[6] USA,undefined
[7] e-mail: biak@cims.nyu.edu,undefined
[8] Courant Institute of Mathematics,undefined
[9] NYU,undefined
[10] 251 Mercer Street,undefined
[11] New York,undefined
[12] NY 10012,undefined
[13] USA,undefined
[14] and Institute of Advanced Study,undefined
[15] Princeton,undefined
[16] NJ 0850,undefined
[17] USA,undefined
[18] e-mail: dieft@cims.nyu.edu,undefined
[19] Department of Mathematics,undefined
[20] Royal Institute of Technology,undefined
[21] S-100 44 Stockholm,undefined
[22] Sweden,undefined
[23] e-mail: kurtj@math.kth.se,undefined
来源：
Geometric & Functional Analysis GAFA | 2000年 / 10卷
关键词：
Probability Distribution; Generate Function; Large Eigenvalue; Young Diagram; Random Permutation;
D O I：
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学科分类号：
摘要：
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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $ N \to \infty $\end{document} 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $ N \to \infty $\end{document} 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.
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页码：702 / 731
页数：29
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