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.Comment: 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
tex
