Random Matrices and Random Permutations

Details Random Matrices and Random Permutations Random Matrices and Random Permutations

1999-03-30

arxiv.org/abs/math/9903176v3

Mathematics

Combinatorics

58 pages, Latex, 32 figures

Scientific paper

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.

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