### 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.

Original language | English |
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Article number | 083509 |

Number of pages | 27 |

Journal | Journal of Mathematical Physics |

Volume | 60 |

Issue number | 8 |

Early online date | 23 Aug 2019 |

DOIs | |

Publication status | Published - 23 Aug 2019 |

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## Cite this

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