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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Ergodic measures on compact metric spaces for isometric actions by inductively compact groups
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by Yanqi Qiu PDF
Proc. Amer. Math. Soc. 145 (2017), 1593-1598 Request permission

Abstract:

We obtain a partial converse of Vershik’s description of ergodic probability measures on a compact metric space with respect to an isometric action by an inductively compact group. This allows us to identify, in this setting, the set of ergodic probability measures with the set of weak limit points of orbital measures. We also show that for a general action of an inductively compact group, the weak limit of orbital measures can fail to be ergodic.
References
  • A. I. Bufetov, Ergodic decomposition for measures quasi-invariant under Borel actions of inductively compact groups, Mat. Sb. 205 (2014), no. 2, 39–70 (Russian, with Russian summary); English transl., Sb. Math. 205 (2014), no. 1-2, 192–219. MR 3204667, DOI 10.1070/sm2014v205n02abeh004371
  • S. V. Kerov, Asymptotic representation theory of the symmetric group and its applications in analysis, Translations of Mathematical Monographs, vol. 219, American Mathematical Society, Providence, RI, 2003. Translated from the Russian manuscript by N. V. Tsilevich; With a foreword by A. Vershik and comments by G. Olshanski. MR 1984868, DOI 10.1090/mmono/219
  • Grigori Olshanski and Anatoli Vershik, Ergodic unitarily invariant measures on the space of infinite Hermitian matrices, Contemporary mathematical physics, Amer. Math. Soc. Transl. Ser. 2, vol. 175, Amer. Math. Soc., Providence, RI, 1996, pp. 137–175. MR 1402920, DOI 10.1090/trans2/175/09
  • Elmar Thoma, Die unzerlegbaren, positiv-definiten Klassenfunktionen der abzählbar unendlichen, symmetrischen Gruppe, Math. Z. 85 (1964), 40–61 (German). MR 173169, DOI 10.1007/BF01114877
  • A. M. Veršik, A description of invariant measures for actions of certain infinite-dimensional groups, Dokl. Akad. Nauk SSSR 218 (1974), 749–752 (Russian). MR 0372161
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Additional Information
  • Yanqi Qiu
  • Affiliation: CNRS, Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 Route de Narbonne, F-31062 Toulouse Cedex 9, France
  • MR Author ID: 989268
  • Email: yqi.qiu@gmail.com
  • Received by editor(s): February 29, 2016
  • Received by editor(s) in revised form: May 25, 2016
  • Published electronically: October 3, 2016
  • Additional Notes: This work is supported by the grant IDEX UNITI - ANR-11-IDEX-0002-02, financed by Programme “Investissements d’Avenir” of the government of the French Republic managed by the French National Research Agency.
  • Communicated by: Nimish Shah
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 1593-1598
  • MSC (2010): Primary 37A25; Secondary 28A33
  • DOI: https://doi.org/10.1090/proc/13371
  • MathSciNet review: 3601550