Random Matrices and Random Permutations

Abstract

We prove the conjecture of Baik, Deift, and Johansson which says that with respect to the Plancherel measure on the set of partitions of $n$, the 1st, 2nd, and so on, rows behave, suitably scaled, like the 1st, 2nd, and so on, eigenvalues of a Gaussian random Hermitian matrix as $n$ goes to infinity. Our proof is based on an interplay between maps on surfaces and ramified coverings of the sphere. We also establish a connection of this problem with intersection theory on the moduli spaces of curves.

58 pages, Latex, 32 figures

References in corpus (3)

• Level-Spacing Distributions and the Airy Kernel
• 2D Gravity and Random Matrices
• On the distribution of the length of the second row of a Young diagram under Plancherel measure

Cited by in corpus (9)

• The uses of random partitions
• Volume of representation varieties
• sl(2) Operators and Markov Processes on Branching Graphs
• A generating function of the number of homomorphisms from a surface group into a finite group
• Integrals over Grassmannians and Random permutations
• Random walks and random permutations
• On the Distribution of the Length of the Longest Increasing Subsequence of Random Permutations
• Stochastic monotonicity in Young graph and Thoma theorem
• Integrals over classical Groups, Random permutations, Toda and Toeplitz lattices