Mixed moments of characteristic polynomials of random unitary matrices editors-pick
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Date
2019
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English
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Abstract
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.
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Bailey, 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/10.1063/1.5092780
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Journal of Mathematical Physics
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ArXiv
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