PLANCHEREL–ROTACH FORMULAE FOR AVERAGE CHARACTERISTIC POLYNOMIALS OF PRODUCTS OF GINIBRE RANDOM MATRICES AND THE FUSS–CATALAN DISTRIBUTION

DOI10.1142/S2010326314500038zbMath1288.30033arXiv1311.0365OpenAlexW2962930287MaRDI QIDQ5416405

Thorsten Neuschel

Publication date: 20 May 2014

Published in: Random Matrices: Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.0365

zbMATH Keywords

asymptotic distribution of zerosPlancherel-Rotach formulaaverage characteristic polynomialsGinibre random matrices

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Multidimensional problems (41A63) Asymptotic representations in the complex plane (30E15)

Related Items (14)

Asymptotics for characteristic polynomials of Wishart type products of complex Gaussian and truncated unitary random matrices ⋮ Singular values for products of complex Ginibre matrices with a source: hard edge limit and phase transition ⋮ Dropping the independence: singular values for products of two coupled random matrices ⋮ Large-dimensional random matrix theory and its applications in deep learning and wireless communications ⋮ Local universality in biorthogonal Laguerre ensembles ⋮ Multiple orthogonal polynomials associated with branched continued fractions for ratios of hypergeometric series ⋮ A Fuss-type family of positive definite sequences ⋮ Relating the Bures measure to the Cauchy two-matrix model ⋮ Spectral densities of singular values of products of Gaussian and truncated unitary random matrices ⋮ Jacobi polynomial moments and products of random matrices ⋮ Characteristic polynomials of products of non-Hermitian Wigner matrices: finite-\(N\) results and Lyapunov universality ⋮ Large \(n\) limit for the product of two coupled random matrices ⋮ Raney distributions and random matrix theory ⋮ Asymptotic zero distribution of Jacobi-Piñeiro and multiple Laguerre polynomials

Cites Work

• On the asymptotic distribution of the zeros of Hermite, Laguerre, and Jonquière polynomials
• On explicit probability densities associated with Fuss-Catalan numbers
• Universal microscopic correlation functions for products of independent Ginibre matrices
• Real Analysis and Probability

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