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.
|Number of pages||33|
|Journal||Annali della Scuola normale superiore di Pisa - Classe di scienze|
|State||Published - 2014|