Geodesic
Infinite determinantal measures and the ergodic decomposition of infinite Pickrell~measures.~III.
Izvestiya. Mathematics , Tome 80 (2016) no. 6, pp. 1035-1056.

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In the third paper of the series we complete the proof of our main result: a description of the ergodic decomposition of infinite Pickrell measures. We first prove that the scaling limit of the determinantal measures corresponding to the radial parts of Pickrell measures is precisely the infinite Bessel process introduced in the first paper of the series. We prove that the ‘Gaussian parameter’ for ergodic components vanishes almost surely. To do this, we associate a finite measure with each configuration and establish convergence to the scaling limit in the space of finite measures on the space of finite measures. We finally prove that the Pickrell measures corresponding to different values of the parameter are mutually singular.
Keywords: weak convergence, the Harish-Chandra–Itzykson–Zuber integral, infinite Bessel process, Jacobi polynomials. 
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A. I. Bufetov. Infinite determinantal measures and the ergodic decomposition of infinite Pickrell~measures.~III.. Izvestiya. Mathematics , Tome 80 (2016) no. 6, pp. 1035-1056. http://geodesic.mathdoc.fr/item/IM2_2016_80_6_a2/

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