Random Strict Partitions and Determinantal Point Processes

Details Random Strict Partitions and Determinantal Point Processes Random Strict Partitions and Determinantal Point Processes

2010-02-13

arxiv.org/abs/1002.2714v3

Electronic Communications in Probability, vol. 15, pp. 162-175, 2010

Mathematics

Probability

LaTeX, 16 pages; v3: typos corrected, Remark 6 (about connections with the z-measures) added

Scientific paper

In this note we present new examples of determinantal point processes with infinitely many particles. The particles live on the half-lattice {1,2,...} or on the open half-line (0,+\infty). The main result is the computation of the correlation kernels. They have integrable form and are expressed through the Euler gamma function (the lattice case) and the classical Whittaker functions (the continuous case). Our processes are obtained via a limit transition from a model of random strict partitions introduced by Borodin (1997) in connection with the problem of harmonic analysis for projective characters of the infinite symmetric group.

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