Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. I. Construction of infinite determinantal measures

A. I. Bufetov

Izvestiya. Mathematics, Tome 79 (2015) no. 6, pp. 1111-1156

Résumé

This paper is the first in a series of three. We give an explicit description of the ergodic decomposition of infinite Pickrell measures on the space of infinite complex matrices. A key role is played by the construction of $\sigma$-finite analogues of determinantal measures on spaces of configurations, including the infinite Bessel process, a scaling limit of the $\sigma$-finite analogues of the Jacobi orthogonal polynomial ensembles. Our main result identifies the infinite Bessel process with the decomposing measure of an infinite Pickrell measure.

Détail

Keywords: determinantal processes, infinite determinantal measures, ergodic decomposition, infinite harmonic analysis, infinite unitary group, scaling limits, Jacobi polynomials, Harish-Chandra–Itzykson–Zuber orbit integral.

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