Moments of Characteristic Polynomials Enumerate Two-Rowed Lexicographic Arrays

E. Strahov

Abstract


A combinatorial interpretation is provided for the moments of characteristic polynomials of random unitary matrices. This leads to a rather unexpected consequence of the Keating and Snaith conjecture: the moments of $|\zeta(1/2+it)|$ turn out to be connected with some increasing subsequence problems (such as the last passage percolation problem).


Full Text: PDF