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This article is cited in 10 scientific papers (total in 10 papers)
The boundary of the orbital beta process
Theodoros Assiotisa, Joseph Najnudelb a School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Rd, Edinburgh EH9 3FD, U.K.
b Laboratoire Mathématiques & Interactions J.A. Dieudonné – Université Côte d'Azur – CNRS UMR 7351 – Parc Valrose 06108 NICE CEDEX 2, France
Abstract:
The unitarily invariant probability measures on infinite Hermitian matrices have been classified by Pickrell and by Olshanski and Vershik. This classification is equivalent to determining the boundary of a certain inhomogeneous Markov chain with given transition probabilities. This formulation of the problem makes sense for general $\beta$-ensembles when one takes as the transition probabilities the Dixon–Anderson conditional probability distribution. In this paper we determine the boundary of this Markov chain for any $\beta \in (0,\infty]$, also giving in this way a new proof of the classical $\beta=2$ case (Pickrell, Olshanski and Vershik). Finally, as a by-product of our results we obtain alternative proofs of the almost sure convergence of the rescaled Hua–Pickrell and Laguerre $\beta$-ensembles to the general $\beta$ Hua–Pickrell and $\beta$ Bessel point processes respectively; these results were obtained earlier by Killip and Stoiciu, Valkó and Virág, Ramírez and Rider.
Key words and phrases:
infinite random matrices, beta ensembles, ergodic measures, boundary of Markov chains.
Citation:
Theodoros Assiotis, Joseph Najnudel, “The boundary of the orbital beta process”, Mosc. Math. J., 21:4 (2021), 659–694
Linking options:
https://www.mathnet.ru/eng/mmj809 https://www.mathnet.ru/eng/mmj/v21/i4/p659
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Abstract page: | 48 | References: | 14 |
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