Markov processes on the path space of the Gelfand–Tsetlin graph and on its boundary
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Borodin_Markov processes on the path.pdf
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Author(s)
Borodin, Alexei
Olshanski, Grigori
Date Issued
April 2012
Journal
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.
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Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-NoDerivatives
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DOI of Published Version
https://doi.org/10.1016/j.jfa.2012.03.018
