Abstract:
The ergodic unitarily invariant measures on the space of infinite Hermitian matrices have been classified by Pickrell and Olshanski–Vershik. The much-studied complex inverse Wishart measures form a projective family, thus giving rise to a unitarily invariant measure on infinite positive-definite matrices. In this paper we completely solve the corresponding problem of ergodic decomposition for this measure.
Keywords:infinite random matrices, ergodic measures, inverse Wishart measures, orthogonal polynomials.
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