Bailey, E. C.Bettin, S.Blower, G.Conrey, J. B.Prokhorov, A.Rubinstein, M. O.Snaith, N. C.2020-02-252020-02-252019Bailey, E. C., Bettin, S., Blower, G., Conrey, J. B., Prokhorov, A., Rubinstein, M. O., & Snaith, N. C. (2019). Mixed moments of characteristic polynomials of random unitary matrices. Journal of Mathematical Physics, 60(8), 083509. https://doi.org/10.1063/1.5092780https://hdl.handle.net/1805/22152Following 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.enPublisher Policymixed momentcharacteristic polynomialrandom unitary matricesArticle