Markov processes on the path space of the Gelfand–Tsetlin graph and on its boundary
Author(s)
Borodin, Alexei; Olshanski, Grigori
DownloadBorodin_Markov processes on the path.pdf (636.5Kb)
PUBLISHER_CC
Publisher with Creative Commons License
Creative Commons Attribution
Terms of use
Metadata
Show full item recordAbstract
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.
Date issued
2012-04Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Journal of Functional Analysis
Publisher
Elsevier
Citation
Borodin, Alexei, and Grigori Olshanski. “Markov Processes on the Path Space of the Gelfand–Tsetlin Graph and on Its Boundary.” Journal of Functional Analysis 263, no. 1 (July 2012): 248–303.
Version: Author's final manuscript
ISSN
00221236
1096-0783