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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Property (T) and the Furstenberg entropy of nonsingular actions
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by Lewis Bowen, Yair Hartman and Omer Tamuz PDF
Proc. Amer. Math. Soc. 144 (2016), 31-39 Request permission

Abstract:

We establish a new characterization of property (T) in terms of the Furstenberg entropy of nonsingular actions. Given any generating measure $\mu$ on a countable group $G$, A. Nevo showed that a necessary condition for $G$ to have property (T) is that the Furstenberg $\mu$-entropy values of the ergodic, properly nonsingular $G$-actions are bounded away from zero. We show that this is also a sufficient condition.
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Additional Information
  • Lewis Bowen
  • Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
  • MR Author ID: 671629
  • Yair Hartman
  • Affiliation: Department of Mathematics, Weizmann Institute of Science, 761001 Rehovot, Israel
  • MR Author ID: 1001252
  • Omer Tamuz
  • Affiliation: Microsoft Research, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • MR Author ID: 898902
  • Received by editor(s): June 30, 2014
  • Received by editor(s) in revised form: December 1, 2014
  • Published electronically: July 24, 2015
  • Additional Notes: The first author was supported in part by NSF grant DMS-0968762, NSF CAREER Award DMS-0954606 and BSF grant 2008274.
    The second author was supported by the European Research Council, grant 239885
  • Communicated by: Nimish Shah
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 31-39
  • MSC (2010): Primary 20F69, 37A40
  • DOI: https://doi.org/10.1090/proc/12685
  • MathSciNet review: 3415574