The z-measures on partitions, Pfaffian point processes, and the matrix hypergeometric kernel
Mathematical Physics
2009-05-14 v1 Combinatorics
math.MP
Abstract
We consider a point process on one-dimensional lattice originated from the harmonic analysis on the infinite symmetric group, and defined by the z-measures with the deformation (Jack) parameter 2. We derive an exact Pfaffian formula for the correlation function of this process. Namely, we prove that the correlation function is given as a Pfaffian with a matrix kernel. The kernel is given in terms of the Gauss hypergeometric functions, and can be considered as a matrix analogue of the Hypergeometric kernel introduced by A. Borodin and G. Olshanski. Our result holds for all values of admissible complex parameters.
Cite
@article{arxiv.0905.1994,
title = {The z-measures on partitions, Pfaffian point processes, and the matrix hypergeometric kernel},
author = {Eugene Strahov},
journal= {arXiv preprint arXiv:0905.1994},
year = {2009}
}
Comments
38 pages