Meixner polynomials and random partitions
| dc.creator | Borodin, Alexei | |
| dc.creator | Olshanski, Grigori | |
| dc.date | 2006-09-28 | |
| dc.date.accessioned | 2026-07-07T07:37:04Z | |
| dc.date.available | 2026-07-07T07:37:04Z | |
| dc.description | 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. The present paper can be viewed as an introduction to another our paper where the same approach is applied to studying a dynamical model related to the z-measures (Markov processes on partitions, Prob. Theory Rel. Fields 135 (2006), 84-152; arXiv: math-ph/0409075). | |
| dc.description | AMSTeX, 27 pages, to appear in Moscow Mathematical Journal | |
| dc.identifier | https://arxiv.org/abs/math/0609806 | |
| dc.identifier | http://arxiv.org/abs/math/0609806 | |
| dc.identifier | Moscow Mathematical Journal 4 (2006), no. 4, 629-655. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120647 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60C05; 60G55; 33C45 | |
| dc.title | Meixner polynomials and random partitions | |
| dc.type | text |