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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IM2_2016_80_6_a2,
     author = {A. I. Bufetov},
     title = {Infinite determinantal measures and the ergodic decomposition of infinite {Pickrell~measures.~III.}},
     journal = {Izvestiya. Mathematics },
     pages = {1035--1056},
     publisher = {mathdoc},
     volume = {80},
     number = {6},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2016_80_6_a2/}
}
TY  - JOUR
AU  - A. I. Bufetov
TI  - Infinite determinantal measures and the ergodic decomposition of infinite Pickrell~measures.~III.
JO  - Izvestiya. Mathematics 
PY  - 2016
SP  - 1035
EP  - 1056
VL  - 80
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2016_80_6_a2/
LA  - en
ID  - IM2_2016_80_6_a2
ER  - 
%0 Journal Article
%A A. I. Bufetov
%T Infinite determinantal measures and the ergodic decomposition of infinite Pickrell~measures.~III.
%J Izvestiya. Mathematics 
%D 2016
%P 1035-1056
%V 80
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2016_80_6_a2/
%G en
%F IM2_2016_80_6_a2
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/