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

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

2010-11-09

arxiv.org/abs/1011.2084v1

Mathematics

Combinatorics

24 pages

Scientific paper

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.

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