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Mixed moments of characteristic polynomials of random unitary matrices (1901.07479v1)
Published 22 Jan 2019 in math-ph, math.MP, and math.NT
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.
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