Pfaffian Stochastic Dynamics of Strict Partitions

Abstract

We study a family of continuous time Markov jump processes on strict partitions (partitions with distinct parts) preserving the distributions introduced by Borodin (1997) in connection with projective representations of the infinite symmetric group. The one-dimensional distributions of the processes (i.e., the Borodin's measures) have determinantal structure. We express the dynamical correlation functions of the processes in terms of certain Pfaffians and give explicit formulas for both the static and dynamical correlation kernels using the Gauss hypergeometric function. Moreover, we are able to express our correlation kernels (both static and dynamical) through those of the z-measures on partitions obtained previously by Borodin and Olshanski in a series of papers. The results about the fixed time case were announced in the author's note arXiv:1002.2714. A part of the present paper contains proofs of those results.

AMS-LaTeX, 59 pages. v2: Added new results about connections with the z-measures and orthogonal spectral projection operators. Investigated asymptotic behaviour of the dynamical Pfaffian correlation kernel. Removed double contour integral expressions for correlation kernels to shorten the text

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Cited by in corpus (1)

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