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.
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’.
Citation:
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
This publication is cited in the following 8 articles:
Alexander I. Bufetov, Yosuke Kawamoto, “The Intertwining Property for Laguerre Processes with a Fixed Parameter”, J Stat Phys, 192:5 (2025)
Assiotis T., “Infinite P-Adic Random Matrices and Ergodic Decomposition of P-Adic Hua Measures”, Trans. Am. Math. Soc., 375:3 (2022), 1745–1766
Theodoros Assiotis, Jonathan P Keating, Jon Warren, “On the Joint Moments of the Characteristic Polynomials of Random Unitary Matrices”, 2022, no. 18, 2022, 14564
Theodoros Assiotis, Benjamin Bedert, Mustafa Alper Gunes, Arun Soor, Prob. Math. Phys., 2:3 (2021), 613
Theodoros Assiotis, “Ergodic Decomposition for Inverse Wishart Measures on Infinite Positive-Definite Matrices”, SIGMA, 15 (2019), 067, 24 pp.
Jorgensen P.E.T., Song M.-S., “Infinite-Dimensional Measure Spaces and Frame Analysis”, Acta Appl. Math., 155:1 (2018), 41–56
Y. Qiu, “Infinite random matrices & ergodic decomposition of finite and infinite Hua-Pickrell measures”, Adv. Math., 308 (2017), 1209–1268
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
Citation in format AMSBIB
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