SHARP DIMENSION FREE QUANTITATIVE ESTIMATES FOR THE GAUSSIAN ISOPERIMETRIC INEQUALITY
成果类型：
Article
署名作者：
Barchiesi, Marco; Brancolini, Alessio; Julin, Vesa
署名单位：
University of Naples Federico II; University of Munster; University of Jyvaskyla
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/15-AOP1072
发表日期：
2017
页码：
668-697
关键词：
摘要：
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.