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This article is cited in 22 scientific papers (total in 22 papers)
Meixner polynomials and random partitions
Alexei Borodina, Grigori Olshanskiib a Mathematics, Caltech, Pasadena, CA, U.S.A.
b Dobrushin Mathematics Laboratory, Institute for Information Transmission Problems, Moscow, RUSSIA
Abstract:
The paper deals with a 3-parameter family of probability measures on the set of partitions, called the z-measures. The z-measures first emerged in connection with the problem of harmonic analysis on the infinite symmetric group. They are a special and distinguished case of Okounkov's Schur measures. It is known that any Schur measure determines a determinantal point process on the 1-dimensional lattice. In the particular case of z-measures, the correlation kernel of this process, called the discrete hypergeometric kernel, has especially nice properties. The aim of the paper is to derive the discrete hypergeometric kernel by a new method, based on a relationship between the z-measures and the Meixner orthogonal polynomial ensemble. In another paper (Prob. Theory Rel. Fields 135 (2006), 84–152) we apply the same approach to a dynamical model related to the z-measures.
Key words and phrases:
Random partitions, random Young diagrams, determinantal point processes, correlation functions, correlation kernels, orthogonal polynomial ensembles, Meixner polynomials, Krawtchouk polynomials.
Received: June 16, 2006
Citation:
Alexei Borodin, Grigori Olshanskii, “Meixner polynomials and random partitions”, Mosc. Math. J., 6:4 (2006), 629–655
Linking options:
https://www.mathnet.ru/eng/mmj263 https://www.mathnet.ru/eng/mmj/v6/i4/p629
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