English

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}
}