Borodin, Alexei and Olshanski, Grigori (2009) Infinite-dimensional diffusions as limits of random walks on partitions. Probability Theory and Related Fields, 144 (1-2). pp. 281-318. ISSN 0178-8051 http://resolver.caltech.edu/CaltechAUTHORS:20090811-133539619
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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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| Additional Information: | © Springer-Verlag 2009. Received: 27 August 2007. Revised: 22 February 2008. Published online: 1 April 2008. Mathematics Subject Classification (2000) 60J60 · 60C05 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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| Subject Keywords: | Diffusion processes; Thoma’s simplex; Infinite symmetric group; Schur functions; z-Measures; Dirichlet forms | ||||||||||||
| Record Number: | CaltechAUTHORS:20090811-133539619 | ||||||||||||
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20090811-133539619 | ||||||||||||
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| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 14963 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | Ruth Sustaita | ||||||||||||
| Deposited On: | 11 Aug 2009 22:52 | ||||||||||||
| Last Modified: | 26 Dec 2012 11:10 |
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