Mixed moments of characteristic polynomials of random unitary matrices
Mathematical Physics
2019-10-02 v1 math.MP
Number Theory
Abstract
Following the work of Conrey, Rubinstein and Snaith and Forrester and Witte we examine a mixed moment of the characteristic polynomial and its derivative for matrices from the unitary group U(N) (also known as the CUE) and relate the moment to the solution of a Painleve differential equation. We also calculate a simple form for the asymptotic behaviour of moments of logarithmic derivatives of these characteristic polynomials evaluated near the unit circle.
Keywords
Cite
@article{arxiv.1901.07479,
title = {Mixed moments of characteristic polynomials of random unitary matrices},
author = {Emma C. Bailey and Sandro Bettin and Gordon Blower and J. Brian Conrey and Andrei Prokhorov and Michael O. Rubinstein and Nina C. Snaith},
journal= {arXiv preprint arXiv:1901.07479},
year = {2019}
}