Perimeters, uniform enlargement and high dimensions
Functional Analysis
2014-11-14 v1 Metric Geometry
Probability
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.
Cite
@article{arxiv.1411.3564,
title = {Perimeters, uniform enlargement and high dimensions},
author = {Franck Barthe and Benoit Huou},
journal= {arXiv preprint arXiv:1411.3564},
year = {2014}
}