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2020 Moments of discrete orthogonal polynomial ensembles
Philip Cohen, Fabio Deelan Cunden, Neil O’Connell
Electron. J. Probab. 25(none): 1-19 (2020). DOI: 10.1214/20-EJP472

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.

Citation

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Philip Cohen. Fabio Deelan Cunden. Neil O’Connell. "Moments of discrete orthogonal polynomial ensembles." Electron. J. Probab. 25 1 - 19, 2020. https://doi.org/10.1214/20-EJP472

Information

Received: 19 September 2019; Accepted: 27 May 2020; Published: 2020
First available in Project Euclid: 1 July 2020

zbMATH: 1444.60010
MathSciNet: MR4119118
Digital Object Identifier: 10.1214/20-EJP472

Subjects:
Primary: 33C45, 60B20

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