Pfaffian Stochastic Dynamics of Strict Partitions
arXiv:1011.3329
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
References in corpus (24)
- The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
- Determinantal Processes and Independence
- Eynard-Mehta theorem, Schur process, and their pfaffian analogs
- Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues
- Correlation functions for symmetrized increasing subsequences
- Infinite-dimensional diffusions as limits of random walks on partitions
- Infinite wedge and random partitions
- Correlation Kernels for Discrete Symplectic and Orthogonal Ensembles
- Pfaffian Expressions for Random Matrix Correlation Functions
- Anisotropic Young diagrams and infinite-dimensional diffusion processes with the Jack parameter
- A Two-Parameter Family of Infinite-Dimensional Diffusions in the Kingman Simplex
- Shifted Schur process and asymptotics of large random strict plane partitions
- Markov processes on partitions
- Non-intersecting Paths, Random Tilings and Random Matrices
- The Dyson Brownian minor process
- The Dimension of Skew Shifted Young Diagrams, and Projective Characters of the Infinite Symmetric Group
- Riemann-Hilbert problem and the discrete Bessel kernel
- On the distribution of the length of the second row of a Young diagram under Plancherel measure
- Non-intersecting, simple, symmetric random walks and the extended Hahn kernel
- Z-measures on partitions related to the infinite Gelfand pair
- Meixner polynomials and random partitions
- Commutation relations and Markov chains
- The z-measures on partitions, Pfaffian point processes, and the matrix hypergeometric kernel
- Random Strict Partitions and Determinantal Point Processes