Distributions on partitions, point processes, and the hypergeometric kernel

Details Distributions on partitions, point processes, and the hypergeometric kernel Distributions on partitions, point processes, and the hypergeometric kernel

1999-04-02

arxiv.org/abs/math/9904010v1

Commun. Math. Phys. 211 (2000), no. 2, 335-358.

Mathematics

Representation Theory

AMSTeX, 24 pages

Scientific paper

10.1007/s002200050815

We study a 3-parametric family of stochastic point processes on the one-dimensional lattice originated from a remarkable family of representations of the infinite symmetric group. We prove that the correlation functions of the processes are given by determinantal formulas with a certain kernel. The kernel can be expressed through the Gauss hypergeometric function; we call it the hypergeometric kernel. In a scaling limit our processes approximate the processes describing the decomposition of representations mentioned above into irreducibles. As we showed before, see math.RT/9810015, the correlation functions of these limit processes also have determinantal form with so-called Whittaker kernel. We show that the scaling limit of the hypergeometric kernel is the Whittaker kernel. The integral operator corresponding to the Whittaker kernel is an integrable operator as defined by Its, Izergin, Korepin, and Slavnov. We argue that the hypergeometric kernel can be considered as a kernel defining a `discrete integrable operator'. We also show that the hypergeometric kernel degenerates for certain values of parameters to the Christoffel-Darboux kernel for Meixner orthogonal polynomials. This fact is parallel to the degeneration of the Whittaker kernel to the Christoffel-Darboux kernel for Laguerre polynomials.

Affiliated with

Also associated with

No associations

Rating

Distributions on partitions, point processes, and the hypergeometric kernel 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 Distributions on partitions, point processes, and the hypergeometric kernel, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Distributions on partitions, point processes, and the hypergeometric kernel will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-110229