Browsing by Subject "characteristic polynomial"

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    Mixed moments of characteristic polynomials of random unitary matrices editors-pick
    (AIP, 2019) Bailey, E. C.; Bettin, S.; Blower, G.; Conrey, J. B.; Prokhorov, A.; Rubinstein, M. O.; Snaith, N. C.; Mathematical Sciences, School of Science
    Following the work of Conrey, Rubinstein, and Snaith [Commun. Math. Phys. 267, 611 (2006)] and Forrester and Witte [J. Phys. A: Math. Gen. 39, 8983 (2006)], 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 Painlevé differential equation. We also calculate a simple form for the asymptotic behavior of moments of logarithmic derivatives of these characteristic polynomials evaluated near the unit circle.