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Dimensionality and the stability of the Brunn-Minkowski inequality

2011/10/30 by Eldan, Ronen, Klartag, Bo`az
#FOS: Mathematics #Metric Geometry (math.MG) #Probability (math.PR)

paper · doi:10.48550/arxiv.1110.6584

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.

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