Meixner polynomials and random partitions

Details Meixner polynomials and random partitions Meixner polynomials and random partitions

2006-09-28

arxiv.org/abs/math/0609806v1

Moscow Mathematical Journal 4 (2006), no. 4, 629-655.

Mathematics

Probability

AMSTeX, 27 pages, to appear in Moscow Mathematical Journal

Scientific paper

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).

Affiliated with

Also associated with

No associations

Rating

Meixner polynomials and random partitions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Meixner polynomials and random partitions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Meixner polynomials and random partitions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-532317