Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 15 (2019), 067, 24 pages      arXiv:1901.03117

Ergodic Decomposition for Inverse Wishart Measures on Infinite Positive-Definite Matrices

Theodoros Assiotis
Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK

Received April 08, 2019, in final form September 04, 2019; Published online September 11, 2019

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.

Key words: infinite random matrices; ergodic measures; inverse Wishart measures; orthogonal polynomials.

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