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

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.

24 pages

References in corpus (2)

• Eynard-Mehta theorem, Schur process, and their pfaffian analogs
• Correlation Kernels for Discrete Symplectic and Orthogonal Ensembles