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Izv. RAN. Ser. Mat., 2016, Volume 80, Issue 2, Pages 16–32 (Mi izv8384)  

This article is cited in 2 scientific papers (total in 2 papers)

Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. II. Convergence of infinite determinantal measures

A. I. Bufetovabcd

a Steklov Mathematical Institute of Russian Academy of Sciences
b National Research University "Higher School of Economics", Moscow
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
d Aix-Marseille Université

Abstract: The second paper in this series is devoted to the convergence of sequences of infinite determinantal measures, understood as the convergence of sequences of the corresponding finite determinantal measures. Besides the weak topology in the space of probability measures on the space of configurations, we also consider the natural immersion (defined almost surely with respect to the infinite Bessel process) of the space of configurations into the space of finite measures on the half-line, which induces a weak topology in the space of finite measures on the space of finite measures on the half-line. The main results of the present paper are sufficient conditions for the tightness of families and the convergence of sequences of induced determinantal processes as well as for the convergence of processes corresponding to finite-rank perturbations of operators.

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

Funding Agency Grant Number
European Research Council 647133
Ministry of Education and Science of the Russian Federation
This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 647133 (ICHAOS)) and has also been funded by the Russian Academic Excellence Project ‘5-100’.


DOI: https://doi.org/10.4213/im8384

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English version:
Izvestiya: Mathematics, 2016, 80:2, 299–315

Bibliographic databases:

UDC: 517.938+519.21
MSC: 20C32, 22D40, 28D15, 43A05, 60B15, 60G55
Received: 07.04.2015
Revised: 16.10.2015

Citation: A. I. Bufetov, “Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. II. Convergence of infinite determinantal measures”, Izv. RAN. Ser. Mat., 80:2 (2016), 16–32; Izv. Math., 80:2 (2016), 299–315

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. A. I. Bufetov, “Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. III. The infinite Bessel process as the limit of the radial parts of finite-dimensional projections of infinite Pickrell measures”, Izv. Math., 80:6 (2016), 1035–1056  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. Y. Qiu, “Infinite random matrices & ergodic decomposition of finite and infinite Hua-Pickrell measures”, Adv. Math., 308 (2017), 1209–1268  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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