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

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.

References in corpus (9)

• Determinantal random point fields
• Level-Spacing Distributions and the Bessel Kernel
• Infinite random matrices and ergodic measures
• Correlators for the Wigner-Smith time-delay matrix of chaotic cavities
• Integer moments of complex Wishart matrices and Hurwitz numbers
• Infinite Determinantal Measures and The Ergodic Decomposition of Infinite Pickrell Measures II. Convergence of determinantal measures
• Infinite Random Matrices and Ergodic decomposition of Finite or Infinite Hua-Pickrell measures
• The Ergodic Decomposition of Infinite Pickrell Measures III. The infinite Bessel process as the limit of radial parts of finite-dimensional projections of infinite Pickrell measures
• Matrix Dufresne Identity

Cited by in corpus (4)

• Matrix Kesten Recursion, Inverse-Wishart Ensemble and Fermions in a Morse Potential
• Convergence and an explicit formula for the joint moments of the Circular Jacobi $\beta$-Ensemble characteristic polynomial
• On a distinguished family of random variables and Painlevé equations
• Infinite p-adic random matrices and ergodic decomposition of p-adic Hua measures