Moments of moments of characteristic polynomials of random unitary matrices and lattice point counts

Author: 

Assiotis, T
Keating, J

Publication Date: 

1 January 2020

Journal: 

Random Matrices: Theory and Application

Last Updated: 

2020-04-10T13:30:56.547+01:00

DOI: 

10.1142/S2010326321500192

abstract: 

© 2021 World Scientific Publishing Company. In this note, we give a combinatorial and noncomputational proof of the asymptotics of the integer moments of the moments of the characteristic polynomials of Haar distributed unitary matrices as the size of the matrix goes to infinity. This is achieved by relating these quantities to a lattice point count problem. Our main result is a new explicit expression for the leading order coefficient in the asymptotic as a volume of a certain region involving continuous Gelfand-Tsetlin patterns with constraints.

Symplectic id: 

1098931

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article