Ergodic decomposition for inverse Wishart measures on infinite positive-definite matrices

Theodoros  Assiotis

doi:10.3842/SIGMA.2019.067

Ergodic decomposition for inverse Wishart measures on infinite positive-definite matrices

Theodoros Assiotis

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	067
Number of pages	24
Journal	Symmetry, Integrability and Geometry : Methods and Applications
Volume	15
DOIs	https://doi.org/10.3842/SIGMA.2019.067
Publication status	Published - 11 Sept 2019

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10.3842/SIGMA.2019.067

1901.03117Final published version, 521 KB

https://arxiv.org/abs/1901.03117

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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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AB - 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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Ergodic decomposition for inverse Wishart measures on infinite positive-definite matrices

Abstract

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