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 2 × 2 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 (2000) . Our result holds for all values of admissible complex parameters.
Bibliographical noteFunding Information:
✩ Supported by US–Israel Binational Science Foundation (BSF), Grant No. 2006333, and by Israel Science Foundation (ISF), Grant No. 0397937. E-mail address: firstname.lastname@example.org.
- Correlation functions
- Pfaffian point processes
- Random partitions
- The Meixner orthogonal polynomials
- Young diagrams