Infinite-dimensional diffusions as limits of random walks on partitions

• 成果类型: Article
• 署名作者: Borodin, Alexei; Olshanski, Grigori
• 署名单位: California Institute of Technology; Kharkevich Institute for Information Transmission Problems of the RAS
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-008-0148-8
• 发表日期: 2009
• 页码: 281-318
• 关键词: point-processes; harmonic-analysis

摘要

Starting with finite Markov chains on partitions of a natural number n we construct, via a scaling limit transition as n -> az, 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.