Dimensionality and the stability of the Brunn-Minkowski inequality
Metric Geometry
2012-08-07 v2 Probability
Abstract
We prove stability estimates for the Brunn-Minkowski inequality for convex sets. Unlike existing stability results, our estimates improve as the dimension grows. Our results are equivalent to a thin shell bound, which is one of the central ingredients in the proof of the central limit theorem for convex sets.
Keywords
Cite
@article{arxiv.1110.6584,
title = {Dimensionality and the stability of the Brunn-Minkowski inequality},
author = {Ronen Eldan and Bo`az Klartag},
journal= {arXiv preprint arXiv:1110.6584},
year = {2012}
}
Comments
27 pages