Monthly Colloquia

Abstract: I provide a combinatorial interpretation of the results obtained by Keating and Snaith for the moments of characteristic polynomials of random unitary matrices.

The goal of the talk is twofold:

i) To describe the relation (Baik, Deift, Johansson and Rains) between random permutations and the Circular Unitary Ensemble of the Random Matrix Theory.

ii) To explain how this relation may be extended to two-rowed lexicographic arrays (generalizations of permutations and words in combinatorics).

Specifically, we shall consider the problem of distribution of the longest increasing subsequence in random two-rowed lexicographic arrays. It will be shown that this combinatorial problem may be reduced to calculation of certain correlation functions of unitary random matrices.