Bernoulli

  • Bernoulli
  • Volume 23, Number 2 (2017), 1056-1081.

Perimeters, uniform enlargement and high dimensions

Franck Barthe and Benoît Huou

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Abstract

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.

Article information

Source
Bernoulli, Volume 23, Number 2 (2017), 1056-1081.

Dates
Received: December 2014
Revised: September 2015
First available in Project Euclid: 4 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.bj/1486177392

Digital Object Identifier
doi:10.3150/15-BEJ769

Mathematical Reviews number (MathSciNet)
MR3606759

Zentralblatt MATH identifier
1378.60012

Keywords
influences isoperimetry

Citation

Barthe, Franck; Huou, Benoît. Perimeters, uniform enlargement and high dimensions. Bernoulli 23 (2017), no. 2, 1056--1081. doi:10.3150/15-BEJ769. https://projecteuclid.org/euclid.bj/1486177392


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