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Mixed moments of characteristic polynomials of random unitary matrices

Research output: Working paper

Published
  • Emma Bailey
  • Sandro Bettin
  • Gordon Blower
  • Brian Conrey
  • Andrey Prokhorov
  • Michael Rubinstein
  • Nina Snaith
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Publication date12/01/2019
Number of pages30
Original languageEnglish

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 Painlev{\'e} 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.