A. I. Bufetov, “Ergodic decomposition for measures quasi-invariant under a Borel action of an inductively compact group”, Sb. Math., 205:2 (2014), 192

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Sbornik: Mathematics, 2014, Volume 205, Issue 2, Pages 192–219
DOI: https://doi.org/10.1070/SM2014v205n02ABEH004371 (Mi sm8202)

This article is cited in 17 scientific papers (total in 17 papers)

Ergodic decomposition for measures quasi-invariant under a Borel action of an inductively compact group

A. I. Bufetov^abcde

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

English version PDF (619 kB) Citations (17) Russian version article

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DOI: https://doi.org/10.1070/SM2014v205n02ABEH004371

Abstract: The aim of this paper is to prove ergodic decomposition theorems for probability measures which are quasi-invariant under Borel actions of inductively compact groups as well as for

σ

$\sigma$ -finite invariant measures. For infinite measures the ergodic decomposition is not unique, but the measure class of the decomposing measure on the space of projective measures is uniquely defined by the initial invariant measure.
Bibliography: 21 titles.

Keywords: ergodic decomposition, infinite-dimensional groups, quasi-invariant measure, infinite-dimensional unitary group, measurable decomposition.

Funding agency	Grant number
Agence Nationale de la Recherche	ANR-11-IDEX-0001-02
Alfred P. Sloan Foundation
Dynasty Foundation
Independent University of Moscow
Ministry of Education and Science of the Russian Federation	MK-6734.2012.1 МД-2859.2014.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Russian Foundation for Basic Research	10-01-93115-NTsNIL 11-01-00654 12-01-31284 12-01-33020 13-01-12449

Received: 21.12.2012 and 26.08.2013

Bibliographic databases:

Document Type: Article

UDC: 517.938

MSC: 28D15, 37A15

Language: English

Original paper language: Russian

Citation: A. I. Bufetov, “Ergodic decomposition for measures quasi-invariant under a Borel action of an inductively compact group”, Sb. Math., 205:2 (2014), 192–219

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/sm8202

https://doi.org/10.1070/SM2014v205n02ABEH004371

https://www.mathnet.ru/eng/sm/v205/i2/p39

This publication is cited in the following 17 articles:

A. I. Bufetov, “Sub-Poissonian estimates for exponential moments of additive functionals over pairs of particles with respect to determinantal and symplectic Pfaffian point processes governed by entire functions”, Mosc. Math. J., 23:4 (2023), 463–478
Vsevolod Zh. Sakbaev, “Flows in infinite-dimensional phase space equipped with a finitely-additive invariant measure”, Mathematics, 11:5 (2023), 1161–49
A. I. Bufetov, “A Palm hierarchy for the decomposing measure in the problem of harmonic analysis on the infinite-dimensional unitary group, the determinantal point process with the confluent hypergeometric kernel”, St. Petersburg Math. J., 35:5 (2024), 769–785
Assiotis T., “Infinite P-Adic Random Matrices and Ergodic Decomposition of P-Adic Hua Measures”, Trans. Am. Math. Soc., 375:3 (2022), 1745–1766
Dello Schiavo L., “Ergodic Decomposition of Dirichlet Forms Via Direct Integrals and Applications”, Potential Anal., 2021
Zaharopol R., “The Ergodic Decomposition Defined By Actions of Amenable Groups”, Colloq. Math., 165:2 (2021), 285–319
T. Assiotis, “Hua-pickrell diffusions and feller processes on the boundary of the graph of spectra”, Ann. Inst. Henri Poincare-Probab. Stat., 56:2 (2020), 1251–1283
Raigorodskii A.M., “On Dividing Sets Into Parts of Smaller Diameter”, Dokl. Math., 102:3 (2020), 510–512
Ya. Qiu, “Ergodic measures on infinite skew-symmetric matrices over non-archimedean local fields”, Group. Geom. Dyn., 13:4 (2019), 1401–1416
Y. Qiu, “Ergodic measures on compact metric spaces for isometric actions by inductively compact groups”, Proc. Amer. Math. Soc., 145:4 (2017), 1593–1598
Y. Qiu, “Infinite random matrices & ergodic decomposition of finite and infinite Hua-Pickrell measures”, Adv. Math., 308 (2017), 1209–1268
A. I. Bufetov, Y. Qiu, “Ergodic measures on spaces of infinite matrices over non-Archimedean locally compact fields”, Compos. Math., 153:12 (2017), 2482–2533
Proc. Steklov Inst. Math., 292 (2016), 94–111
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, “Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. I. Construction of infinite determinantal measures”, Izv. Math., 79:6 (2015), 1111–1156
A. I. Bufetov, “Finiteness of ergodic unitarily invariant measures on spaces of infinite matrices”, Ann. Inst. Fourier, 64:3 (2014), 893–907

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	836
Russian version PDF:	344
English version PDF:	50
References:	144
First page:	94

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