Open Access
May 2017 Perimeters, uniform enlargement and high dimensions
Franck Barthe, Benoît Huou
Bernoulli 23(2): 1056-1081 (May 2017). DOI: 10.3150/15-BEJ769


We study the isoperimetric problem in product spaces equipped with the uniform distance. Our main result is a characterization of isoperimetric inequalities which, when satisfied on a space, are still valid for the product spaces, up a to a constant which does not depend on the number of factors. Such dimension free bounds have applications to the study of influences of variables.


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Franck Barthe. Benoît Huou. "Perimeters, uniform enlargement and high dimensions." Bernoulli 23 (2) 1056 - 1081, May 2017.


Received: 1 December 2014; Revised: 1 September 2015; Published: May 2017
First available in Project Euclid: 4 February 2017

zbMATH: 1378.60012
MathSciNet: MR3606759
Digital Object Identifier: 10.3150/15-BEJ769

Keywords: Influences , Isoperimetry

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 2 • May 2017
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