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2005 Distributions of Invariant Ensembles from the Classical Orthogonal Polynimials: the Discrete Case
Michel Ledoux
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Electron. J. Probab. 10: 1116-1146 (2005). DOI: 10.1214/EJP.v10-282

Abstract

We examine the Charlier, Meixner, Krawtchouk and Hahn discrete orthogonal polynomial ensembles, deeply investigated by K. Johansson, using integration by parts for the underlying Markov operators, differential equations on Laplace transforms and moment equations. As for the matrix ensembles, equilibrium measures are described as limits of empirical spectral distributions. In particular, a new description of the equilibrium measures as adapted mixtures of the universal arcsine law with an independent uniform distribution is emphasized. Factorial moment identities on mean spectral measures may be used towards small deviation inequalities on the rightmost charges at the rate given by the Tracy-Widom asymptotics.

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Michel Ledoux. "Distributions of Invariant Ensembles from the Classical Orthogonal Polynimials: the Discrete Case." Electron. J. Probab. 10 1116 - 1146, 2005. https://doi.org/10.1214/EJP.v10-282

Information

Accepted: 9 September 2005; Published: 2005
First available in Project Euclid: 1 June 2016

zbMATH: 1110.60091
MathSciNet: MR2164041
Digital Object Identifier: 10.1214/EJP.v10-282

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