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 |
| State | Published - 2014 |