Perimeters, uniform enlargement and high dimensions

Franck Barthe; Benoît Huou

doi:10.3150/15-BEJ769

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Home > Journals > Bernoulli > Volume 23 > Issue 2 > Article

May 2017 Perimeters, uniform enlargement and high dimensions

Franck Barthe, Benoît Huou

Bernoulli 23(2): 1056-1081 (May 2017). DOI: 10.3150/15-BEJ769

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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.

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Franck Barthe. Benoît Huou. "Perimeters, uniform enlargement and high dimensions." Bernoulli 23 (2) 1056 - 1081, May 2017. https://doi.org/10.3150/15-BEJ769