This article is cited in 3 scientific papers (total in 3 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
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.
determinantal processes, infinite determinantal measures, ergodic decomposition,
infinite-dimensional harmonic analysis, infinite unitary group, scaling limits,
Jacobi polynomials, Harish-Chandra–Itzykson–Zuber orbit integral.
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Izvestiya: Mathematics, 2016, 80:2, 299–315
MSC: 20C32, 22D40, 28D15, 43A05, 60B15, 60G55
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
\paper Infinite determinantal measures and the ergodic decomposition of infinite
Pickrell measures. II.~Convergence 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. 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
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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