Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality

• Marco Barchiesi ^[3] ; Alessio Brancolini ^[1] ; Vesa Julin ^[2]
  1. [1] University of Münster

     University of Münster

     Kreisfreie Stadt Münster, Alemania

     
  2. [2] University of Jyväskylä

     University of Jyväskylä

     Jyväskylä, Finlandia

     
  3. [3] Università di Napoli "Federico II"

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• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 2, 2017, págs. 668-697
• Idioma: inglés
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• Resumen

  • We provide a full quantitative version of the Gaussian isoperimetric inequality: the difference between the Gaussian perimeter of a given set and a half-space with the same mass controls the gap between the norms of the corresponding barycenters. In particular, it controls the Gaussian measure of the symmetric difference between the set and the half-space oriented so to have the barycenter in the same direction of the set. Our estimate is independent of the dimension, sharp on the decay rate with respect to the gap and with optimal dependence on the mass.