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 βensembles when one takes as the transition probabilities the DixonAnderson conditional probability distribution. In this paper we determine the boundary of this Markov chain for any β∈(0,∞], also giving in this way a new proof of the classical β=2 case. Finally, as a byproduct of our results we obtain alternative proofs of the almost sure convergence of the rescaled HuaPickrell and Laguerre βensembles to the general β HuaPickrell and β Bessel point processes respectively.
Original language  English 

Publisher  ArXiv 
Publication status  Published  20 Aug 2020 
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Theo Assiotis
 School of Mathematics  Lectureship/Readership in Probability and Stochastic Analysi
Person: Academic: Research Active (Teaching)