Pfaffian L-ensembles related to the z-measures on partitions with the Jack parameters 1/2 or 2

TL;DR

This paper constructs Pfaffian L-ensembles linked to z-measures and Jack parameter partitions, showing these measures induce Pfaffian point processes with explicit correlation kernels.

Contribution

It introduces new Pfaffian L-ensembles associated with specific measures on partitions and derives explicit formulas for their correlation kernels.

Findings

Measures induce Pfaffian point processes

Explicit formulas for L-matrices and kernels

Connections between z-measures, Jack parameters, and Pfaffian structures

Abstract

We construct Pfaffian L-ensembles related to the z-measures on partitions and to the Plancherel measures on partitions with the Jack parameters 1/2 or 2. The results imply that these measures on partitions lead to Pfaffian point processes, and the correlation kernels of these processes can be expressed in terms of the corresponding L-matrices. We give explit formulae for these L-matrices.