This article is cited in 6 scientific papers (total in 6 papers)
Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. I. Construction of infinite determinantal measures
A. I. Bufetovabcd
a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
c National Research University "Higher School of Economics" (HSE), Moscow
d Aix-Marseille Université
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.
determinantal processes, infinite determinantal measures, ergodic decomposition,
infinite harmonic analysis, infinite unitary group, scaling limits,
Jacobi polynomials, Harish-Chandra–Itzykson–Zuber orbit integral.
|Agence Nationale de la Recherche
|Ministry of Education and Science of the Russian Federation
|Russian Academy of Sciences - Federal Agency for Scientific Organizations
|Russian Foundation for Basic Research
|This work was supported by the project A*MIDEX (no. ANR-11-IDEX-0001-02)
of the French Republic Government Programme ‘Investing in the Future’ carried
out by the French National Agency of Scientific Research (ANR). It was also
supported by the Programme of Governmental Support of Scientific Research
of Young Russian Scholars, Candidates and Doctors of Sciences (grant
no. MD-2859.2014.1), the Programme of Fundamental Research of RAS
no. I.28P ‘Mathematical problems of modern control theory’
(project no. 0014-2015-0006 ‘Ergodic theory and dynamical systems’),
the subsidy for governmental support of leading universities of the Russian
Federation aimed at raising their competitiveness among world leading
scientific and educational centres, distributed to the National Research
University ‘Higher School of Economics’,
and the RFBR (grant no. 13-01-12449-ofi_m).
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Izvestiya: Mathematics, 2015, 79:6, 1111–1156
MSC: 20C32, 22D40, 28C10, 28D15, 43A05, 60B15, 60G55
A. I. Bufetov, “Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. I. Construction of infinite determinantal measures”, Izv. RAN. Ser. Mat., 79:6 (2015), 18–64; Izv. Math., 79:6 (2015), 1111–1156
Citation in format AMSBIB
\paper Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. I. Construction of infinite determinantal measures
\jour Izv. RAN. Ser. Mat.
\jour Izv. Math.
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This publication is cited in the following articles:
A. I. Bufetov, “Infinite determinantal measures and the ergodic decomposition of infinite
Pickrell measures. II. Convergence of infinite determinantal measures”, Izv. Math., 80:2 (2016), 299–315
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
A. I. Bufetov, Y. Qiu, “The explicit formulae for scaling limits in the ergodic decomposition of infinite Pickrell measures”, Ark. Mat., 54:2 (2016), 403–435
Alexander I. Bufetov, “A Palm hierarchy for determinantal point processes with the Bessel kernel”, Proc. Steklov Inst. Math., 297 (2017), 90–97
Y. Qiu, “Infinite random matrices & ergodic decomposition of finite and infinite Hua-Pickrell measures”, Adv. Math., 308 (2017), 1209–1268
Theodoros Assiotis, “Ergodic Decomposition for Inverse Wishart Measures on Infinite Positive-Definite Matrices”, SIGMA, 15 (2019), 067, 24 pp.
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