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Stability of Talagrand's inequality under concentration topology


Authors: Ryunosuke Ozawa and Norihiko Suzuki
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 53C23; Secondary 60E15
DOI: https://doi.org/10.1090/proc/13580
Published electronically: April 27, 2017
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Abstract: In this paper, we study the compatibility between Talagrand's inequality and the concentration topology; i.e., if a sequence of mm-spaces satisfying Talagrand's inequality converges with respect to the observable distance, then the limit space satisfies Talagrand's inequality.


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Additional Information

Ryunosuke Ozawa
Affiliation: Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany
Address at time of publication: Department of Mathematics, Osaka University, Osaka 560-0043, Japan
Email: r.ozawa@cr.math.sci.osaka-u.ac.jp

Norihiko Suzuki
Affiliation: Mathematical Institute, Tohoku University, Sendai 980-8578, Japan
Email: norihiko.suzuki.p5@dc.tohoku.ac.jp

DOI: https://doi.org/10.1090/proc/13580
Keywords: Metric measure space, observable distance, Talagrand's inequality
Received by editor(s): July 18, 2016
Received by editor(s) in revised form: November 1, 2016
Published electronically: April 27, 2017
Additional Notes: The first author was supported by JSPS KAKENHI Grant No. 24224002 and postdoctoral program at Max Planck Institute for Mathematics.
Communicated by: Mark M. Meerschaert
Article copyright: © Copyright 2017 American Mathematical Society