English

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}
}

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27 pages