Wigner matrices, the moments of roots of Hermite polynomials and the semicircle law

DOI10.1016/j.jat.2016.07.006zbMath1350.15024arXiv1512.03724OpenAlexW2963486088MaRDI QIDQ320330

Miklós Kornyik, György Michaletzky

Publication date: 6 October 2016

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.03724

zbMATH Keywords

Catalan numbercharacteristic polynomialrandom matrixWigner matrixmoments of roots of Hermite polynomialsnormalized eigenvaluessemicircle law

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52)

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Cites Work

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• On the asymptotic distribution of the zeros of Hermite, Laguerre, and Jonquière polynomials
• Convergence to the semicircle law
• On sums of powers of zeros of polynomials
• Average characteristic polynomials of determinantal point processes
• Counting formulas associated with some random matrix averages
• On the asymptotic distribution of the eigenvalues of random matrices
• Spectral theory of random matrices
• Characteristic polynomials of random matrices.
• On asymptotic zero distribution of Laguerre and generalized Bessel polynomials with varying parameters

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