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arXiv · 0905.1994

The z-measures on partitions, Pfaffian point processes, and the matrix hypergeometric kernel

Eugene Strahov
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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.

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Eugene Strahov. 2009-05-13. The z-measures on partitions, Pfaffian point processes, and the matrix hypergeometric kernel. https://arxiv.org/abs/0905.1994

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