Dimensionality and the stability of the Brunn-Minkowski inequality

• Ronen Eldan ^[1] ; Boaz Klartag ^[1]
  1. [1] Tel-Aviv University, Israel
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 13, Nº 4, 2014, págs. 975-1007
• Idioma: inglés
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• Resumen

  • 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 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.