Moments of discrete orthogonal polynomial ensembles
Abstract
We obtain factorial moment identities for the Charlier, Meixner and Krawtchouk orthogonal polynomial ensembles. Building on earlier results by Ledoux [Elect. J. Probab. 10, (2005)], we find hypergeometric representations for the factorial moments when the reference measure is Poisson (Charlier ensemble) and geometric (a particular case of the Meixner ensemble). In these cases, if the number of particles is suitably randomised, the factorial moments have a polynomial property, and satisfy three-term recurrence relations and differential equations. In particular, the normalised factorial moments of the randomised ensembles are precisely related to the moments of the corresponding equilibrium measures. We also briefly outline how these results can be interpreted as Cauchy-type identities for certain Schur measures.
Keywords
Cite
@article{arxiv.1907.12884,
title = {Moments of discrete orthogonal polynomial ensembles},
author = {Philip Cohen and Fabio Deelan Cunden and Neil O'Connell},
journal= {arXiv preprint arXiv:1907.12884},
year = {2020}
}
Comments
20 pages