Emma C. Bailey, Sandro Bettin, Gordon Blower, J. Brian Conrey, Andrei Prokhorov, Michael O. Rubinstein, Nina C. Snaith
Published 2019-01-22Version 1
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.
Moments of the derivative of the characteristic polynomial of unitary matrices
A few remarks on Colour-Flavour Transformations,truncations of random unitary matrices, Berezin reproducing kernels and Selberg type integrals
Volumes of orthogonal groups and unitary groups
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