Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials. The continuous case.
Ledoux, M. (2004)
Electronic Journal of Probability [electronic only]
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Ledoux, M. (2004)
Electronic Journal of Probability [electronic only]
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König, Wolfgang (2005)
Probability Surveys [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...
Thomas Bloom (2007)
Annales Polonici Mathematici
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For certain ensembles of random polynomials we give the expected value of the zero distribution (in one variable) and the expected value of the distribution of common zeros of m polynomials (in m variables).
Denys Pommeret (2007)
ESAIM: Probability and Statistics
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For any given random variable with infinitely divisible distribution in a quadratic natural exponential family we obtain a polynomial expansion of the power mixture density of . We approach the problem generally, and then consider certain distributions in greater detail. Various applications are indicated and the results are also applied to obtain approximations and their error bounds. Estimation of density and goodness-of-fit test are derived.
Matsumoto, Sho (2008)
The Electronic Journal of Combinatorics [electronic only]
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Lee, P.A. (1980)
International Journal of Mathematics and Mathematical Sciences
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Posfai, Anna (2009)
Electronic Communications in Probability [electronic only]
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Sznitman, Alain-Sol (2009)
Electronic Journal of Probability [electronic only]
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Lozada-Chang, Li-Vang (2005)
Electronic Journal of Probability [electronic only]
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Charris, Jairo A., Soriano, Felix H. (1996)
International Journal of Mathematics and Mathematical Sciences
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Diaconis, Persi, Gamburd, Alex (2004)
The Electronic Journal of Combinatorics [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.