Abstract
Starting with finite Markov chains on partitions of a natural number n we construct, via a scaling limit transition as n → ∞, a family of infinite-dimensional diffusion processes. The limit processes are ergodic; their stationary distributions, the so-called z-measures, appeared earlier in the problem of harmonic analysis for the infinite symmetric group. The generators of the processes are explicitly described.
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Borodin, A., Olshanski, G. Infinite-dimensional diffusions as limits of random walks on partitions. Probab. Theory Relat. Fields 144, 281–318 (2009). https://doi.org/10.1007/s00440-008-0148-8
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DOI: https://doi.org/10.1007/s00440-008-0148-8
Keywords
- Diffusion processes
- Thoma’s simplex
- Infinite symmetric group
- Schur functions
- z-Measures
- Dirichlet forms
Mathematics Subject Classification (2000)
- 60J60
- 60C05