Electronic Journal of Probability

Moments of discrete orthogonal polynomial ensembles

Philip Cohen, Fabio Deelan Cunden, and Neil O’Connell

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 25 (2020), paper no. 72, 19 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1593568836

Digital Object Identifier
doi:10.1214/20-EJP472

Mathematical Reviews number (MathSciNet)
MR4119118

Zentralblatt MATH identifier
07225526

Subjects
Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52) 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions]

Keywords
random matrices factorial moments Charlier, Meixner and Krawtchouk polynomials hypergeometric functions

Rights
Creative Commons Attribution 4.0 International License.

Citation

Cohen, Philip; Deelan Cunden, Fabio; O’Connell, Neil. Moments of discrete orthogonal polynomial ensembles. Electron. J. Probab. 25 (2020), paper no. 72, 19 pp. doi:10.1214/20-EJP472. https://projecteuclid.org/euclid.ejp/1593568836


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