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arXiv · 1901.07479

Mixed moments of characteristic polynomials of random unitary matrices

Emma C. Bailey·Sandro Bettin·Gordon Blower·J. Brian Conrey·Andrei Prokhorov·Michael O. Rubinstein·Nina C. Snaith
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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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Emma C. Bailey, Sandro Bettin, Gordon Blower, J. Brian Conrey, Andrei Prokhorov, Michael O. Rubinstein, Nina C. Snaith. 2019-01-22. Mixed moments of characteristic polynomials of random unitary matrices. https://doi.org/10.1063/1.5092780

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