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

Theodoros Assiotis

Type: Article

Publication Date: 2019-09-11

Citations: 9

DOI: https://doi.org/10.3842/sigma.2019.067

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.

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