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Published May 2009 | Submitted
Journal Article Open

Infinite-dimensional diffusions as limits of random walks on partitions

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.

Additional Information

© Springer-Verlag 2009. Received: 27 August 2007. Revised: 22 February 2008. Published online: 1 April 2008. The present research was supported by the CRDF grant RUM1-2622-ST-04 (both authors), by the NSF grants DMS-0402047 and DMS-0707163 (A. Borodin), and by the RFBR grant 07-01-91209 and SFB 701, University of Bielefeld (G. Olshanski). G. Olshanski is deeply grateful to Yuri Kondratiev and Michael Röckner for hospitality in Bielefeld and fruitful discussions.

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