Displaying similar documents to “Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials. The continuous case.”

A recursion formula for the moments of the gaussian orthogonal ensemble

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...

The rate of convergence for spectra of GUE and LUE matrix ensembles

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.

Discrete limit theorems for general Dirichlet series. III

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.