Mixed moments of characteristic polynomials of random unitary matrices

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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Cited by in corpus (8)

• Characteristic polynomials of complex random matrices and Painlevé transcendents
• A representation of joint moments of CUE characteristic polynomials in terms of Painleve functions
• Joint moments of a characteristic polynomial and its derivative for the circular $\beta$-ensemble
• Convergence and an explicit formula for the joint moments of the Circular Jacobi $\beta$-Ensemble characteristic polynomial
• Moments of the logarithmic derivative of characteristic polynomials from $SO(N)$ and $USp(2N)$
• Joint moments of derivatives of characteristic polynomials of random symplectic and orthogonal matrices
• On a distinguished family of random variables and Painlevé equations
• On the logarithmic derivative of characteristic polynomials for random unitary matrices