Joint moments of higher order derivatives of CUE characteristic polynomials. II: Structures, recursive relations, and applications

DOI10.1088/1361-6544/ad5948zbMATH Open1543.1503MaRDI QIDQ6566572

Jonathan P. Keating, Fei Wei

Publication date: 3 July 2024

Published in: Nonlinearity (Search for Journal in Brave)

zbMATH Keywords

Young diagramsHankel determinantshigher order derivativesjoint moments\(\sigma\)-Painlevé III' equationCUE characteristic polynomialsI-Bessel functions

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Random matrices (algebraic aspects) (15B52) Relations with random matrices (11M50)

Cites Work

• Unnamed Item
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• Joint moments of derivatives of characteristic polynomials
• Fredholm determinants, differential equations and matrix models
• The theory of the \(G\)-function.
• Painlevé II in random matrix theory and related fields
• Moments of the derivative of characteristic polynomials with an application to the Riemann zeta function
• Formulas for the Evaluation of Toeplitz Determinants with Rational Generating Functions
• Application of the τ‐function theory of Painlevé equations to random matrices: P_V, P_III, the LUE, JUE, and CUE
• On the Joint Moments of the Characteristic Polynomials of Random Unitary Matrices
• Mixed moments of characteristic polynomials of random unitary matrices
• A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions
• Boundary conditions associated with the Painlevé III′ and V evaluations of some random matrix averages
• Application of the \(\tau\)-function theory of Painlevé equations to random matrices: PIV, PII and the GUE.
• Random matrix theory and \(\zeta(1/2+it)\).
• Joint moments of higher order derivatives of CUE characteristic polynomials. I: Asymptotic formulae

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