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 talk I will explain all of the above and how to solve the problem in the beta ensemble setting. This is joint work with Joseph Najnudel.
