Distributions of Invariant Ensembles from the Classical Orthogonal Polynimials: the Discrete Case
Michel Ledoux, Université Toulouse
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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