Dimensionality and the stability of the Brunn-Minkowski inequality

Ronen Eldan, Bo'az Klartag

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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 languageEnglish
Pages (from-to)975-1007
Number of pages33
JournalAnnali della Scuola normale superiore di Pisa - Classe di scienze
Issue number4
StatePublished - 2014


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