Electronic Journal of Probability
- Electron. J. Probab.
- Volume 16 (2011), paper no. 82, 2246-2295.
Pfaffian Stochastic Dynamics of Strict Partitions
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 note [El. Comm. Probab., 15 (2010), 162-175]. A part of the present paper contains proofs of those results.
Electron. J. Probab. Volume 16 (2011), paper no. 82, 2246-2295.
Accepted: 15 November 2011
First available in Project Euclid: 1 June 2016
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Petrov, Leonid. Pfaffian Stochastic Dynamics of Strict Partitions. Electron. J. Probab. 16 (2011), paper no. 82, 2246--2295. doi:10.1214/EJP.v16-956. https://projecteuclid.org/euclid.ejp/1464820251