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Moments of discrete orthogonal polynomial ensembles. (English) Zbl 1444.60010

Summary: We obtain factorial moment identities for the Charlier, Meixner and Krawtchouk orthogonal polynomial ensembles. Building on earlier results by M. Ledoux [ibid. 10, Paper No. 34, 1116–1146 (2005; Zbl 1110.60091)], 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.

MSC:

60B20 Random matrices (probabilistic aspects)
15B52 Random matrices (algebraic aspects)
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

Citations:

Zbl 1110.60091
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References:

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