Random Strict Partitions and Determinantal Point Processes

Abstract

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.

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

References in corpus (6)

• Infinite-dimensional diffusions as limits of random walks on partitions
• A Limit Theorem for Shifted Schur Measures
• Shifted Schur process and asymptotics of large random strict plane partitions
• The Dimension of Skew Shifted Young Diagrams, and Projective Characters of the Infinite Symmetric Group
• Z-measures on partitions related to the infinite Gelfand pair $(S(2\infty ),H(\infty ))$
• The z-measures on partitions, Pfaffian point processes, and the matrix hypergeometric kernel

Cited by in corpus (2)

• Pfaffian Stochastic Dynamics of Strict Partitions
• On Measures on Partitions Arising in Harmonic Analysis for Linear and Projective Characters of the Infinite Symmetric Group