Geodesic
Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. I. Construction of infinite determinantal measures
Izvestiya. Mathematics , Tome 79 (2015) no. 6, pp. 1111-1156

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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.
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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     author = {A. I. Bufetov},
     title = {Infinite determinantal measures and the ergodic decomposition of infinite {Pickrell} measures. {I.} {Construction} of infinite determinantal measures},
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     url = {http://geodesic.mathdoc.fr/item/IM2_2015_79_6_a1/}
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A. I. Bufetov. Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. I. Construction of infinite determinantal measures. Izvestiya. Mathematics , Tome 79 (2015) no. 6, pp. 1111-1156. http://geodesic.mathdoc.fr/item/IM2_2015_79_6_a1/