Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials: the discrete case.
Ledoux, M. (2005)
Electronic Journal of Probability [electronic only]
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Ledoux, M. (2005)
Electronic Journal of Probability [electronic only]
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M. Ledoux (2009)
Annales de l'I.H.P. Probabilités et statistiques
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We present an analogue of the Harer–Zagier recursion formula for the moments of the gaussian Orthogonal Ensemble in the form of a five term recurrence equation. The proof is based on simple gaussian integration by parts and differential equations on Laplace transforms. A similar recursion formula holds for the gaussian Symplectic Ensemble. As in the complex case, the result is interpreted as a recursion formula for the number of 1-vertex maps in locally orientable surfaces with a given...
König, Wolfgang (2005)
Probability Surveys [electronic only]
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da Fonseca, C.M., Petronilho, J. (2004)
International Journal of Mathematics and Mathematical Sciences
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Houdré, Christian, Xu, Hua (2008)
Electronic Journal of Probability [electronic only]
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Matsumoto, Sho (2008)
The Electronic Journal of Combinatorics [electronic only]
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Friedrich Götze, Alexander Tikhomirov (2005)
Open Mathematics
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We obtain optimal bounds of order O(n −1) for the rate of convergence to the semicircle law and to the Marchenko-Pastur law for the expected spectral distribution functions of random matrices from the GUE and LUE, respectively.
Diaconis, Persi, Gamburd, Alex (2004)
The Electronic Journal of Combinatorics [electronic only]
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Dette, Holger, Reuther, Bettina (2010)
Journal of Probability and Statistics
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Guionnet, Alice (2004)
Probability Surveys [electronic only]
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A. Laurinčikas, R. Macaitienė (2004)
Open Mathematics
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Here we prove a limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for a general Dirichlet series. The explicit form of the limit measure in this theorem is given.
Barry, Paul (2011)
Journal of Integer Sequences [electronic only]
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