Infinite determinantal measures

Alexander I. Bufetov

doi:10.3934/era.2013.20.12

Article Contents

2013, Volume 20: 12-30. Doi: 10.3934/era.2013.20.12

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Infinite determinantal measures

Alexander I. Bufetov^1,

1.
Laboratoire d'Analyse, Topologie, Probabilités, Aix-Marseille Université, CNRS, Marseille

Received: June 30, 2012

Revised: October 31, 2012

Published: December 2012

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Abstract

Infinite determinantal measures introduced in this note are inductive limits of determinantal measures on an exhausting family of subsets of the phase space. Alternatively, an infinite determinantal measure can be described as a product of a determinantal point process and a convergent, but not integrable, multiplicative functional.
Theorem 4.1, the main result announced in this note, gives an explicit description for the ergodic decomposition of infinite Pickrell measures on the spaces of infinite complex matrices in terms of infinite determinantal measures obtained by finite-rank perturbations of Bessel point processes.

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Mathematics Subject Classification: Primary: 60G60; Secondary: 37A15.

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