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Infinite-dimensional diffusions as limits of random walks on partitions
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  • Published: 01 April 2008

Infinite-dimensional diffusions as limits of random walks on partitions

  • Alexei Borodin1 &
  • Grigori Olshanski2 

Probability Theory and Related Fields volume 144, pages 281–318 (2009)Cite this article

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  • 37 Citations

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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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Author information

Authors and Affiliations

  1. Mathematics 253-37, Caltech, Pasadena, CA, 91125, USA

    Alexei Borodin

  2. Dobrushin Mathematics Laboratory, Institute for Information Transmission Problems, Bolshoy Karetny 19, 127994, Moscow GSP-4, Russia

    Grigori Olshanski

Authors
  1. Alexei Borodin
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  2. Grigori Olshanski
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Correspondence to Alexei Borodin.

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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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  • Received: 27 August 2007

  • Revised: 22 February 2008

  • Published: 01 April 2008

  • Issue Date: May 2009

  • DOI: https://doi.org/10.1007/s00440-008-0148-8

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Keywords

  • Diffusion processes
  • Thoma’s simplex
  • Infinite symmetric group
  • Schur functions
  • z-Measures
  • Dirichlet forms

Mathematics Subject Classification (2000)

  • 60J60
  • 60C05
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