Published July 1, 2012
| public
Journal Article
Markov processes on the path space of the Gelfand–Tsetlin graph and on its boundary
- Creators
- Borodin, Alexei
- Olshanski, Grigori
Abstract
We construct a four-parameter family of Markov processes on infinite Gelfand–Tsetlin schemes that preserve the class of central (Gibbs) measures. Any process in the family induces a Feller Markov process on the infinite-dimensional boundary of the Gelfand–Tsetlin graph or, equivalently, the space of extreme characters of the infinite-dimensional unitary group U(∞). The process has a unique invariant distribution which arises as the decomposing measure in a natural problem of harmonic analysis on U(∞) posed in Olshanski (2003) [44]. As was shown in Borodin and Olshanski (2005) [11], this measure can also be described as a determinantal point process with a correlation kernel expressed through the Gauss hypergeometric function.
Additional Information
© 2012 Elsevier Inc. Received 30 November 2011. Accepted 20 March 2012. Available online 11 April 2012. Communicated by D. Voiculescu. A.B. was partially supported by NSF grants DMS-0707163 and DMS-1056390. G.O. was partially supported by the RFBR grant 08-01-00110, the RFBR-CNRS grant 10-01-93114, the project SFB 701 of Bielefeld University, and a grant from Simons Foundation (Simons–IUM Fellowship).Additional details
- Eprint ID
- 31911
- Resolver ID
- CaltechAUTHORS:20120614-131037267
- DMS-0707163
- NSF
- DMS-1056390
- NSF
- 08-01-00110
- RFBR
- 10-01-93114
- RFBR-CNRS
- Bielefeld University
- Simons Foundation
- Created
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2012-06-18Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field