Year: 1999
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Okounkov, Andrei
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2042682665