Dimensionality and the stability of the Brunn-Minkowski inequality

Ronen Eldan; Bo'az Klartag

Dimensionality and the stability of the Brunn-Minkowski inequality

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Abstract

We prove stability estimates for the Brunn-Minkowski inequality for convex sets. As opposed to previous stability results, our estimates improve as the dimension grows. In particular, we obtain a non-trivial conclusion for high dimensions already when (Equation Presented) 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.

Original language	English
Pages (from-to)	975-1007
Number of pages	33
Journal	Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Volume	13
Issue number	4
Early online date	23 Dec 2014
State	Published - 2014

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Mathematics (miscellaneous)

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Cite this

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title = "Dimensionality and the stability of the Brunn-Minkowski inequality",

abstract = "We prove stability estimates for the Brunn-Minkowski inequality for convex sets. As opposed to previous stability results, our estimates improve as the dimension grows. In particular, we obtain a non-trivial conclusion for high dimensions already when (Equation Presented) 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.",

author = "Ronen Eldan and Bo'az Klartag",

note = "Supported in part by the Israel Science Foundation and by a Marie Curie Reintegration Grant from the Commission of the European Communities.",

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AU - Klartag, Bo'az

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PY - 2014

Y1 - 2014

N2 - We prove stability estimates for the Brunn-Minkowski inequality for convex sets. As opposed to previous stability results, our estimates improve as the dimension grows. In particular, we obtain a non-trivial conclusion for high dimensions already when (Equation Presented) 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.

AB - We prove stability estimates for the Brunn-Minkowski inequality for convex sets. As opposed to previous stability results, our estimates improve as the dimension grows. In particular, we obtain a non-trivial conclusion for high dimensions already when (Equation Presented) 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.

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M3 - مقالة

SN - 0391-173X

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SP - 975

EP - 1007

JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

JF - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

IS - 4

ER -

Dimensionality and the stability of the Brunn-Minkowski inequality

Abstract

All Science Journal Classification (ASJC) codes

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