The Annals of Probability

Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality

Marco Barchiesi, Alessio Brancolini, and Vesa Julin

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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.

Article information

Ann. Probab., Volume 45, Number 2 (2017), 668-697.

Received: April 2015
Revised: October 2015
First available in Project Euclid: 31 March 2017

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Zentralblatt MATH identifier

Primary: 49Q20: Variational problems in a geometric measure-theoretic setting
Secondary: 60E15: Inequalities; stochastic orderings

Quantitative estimates Gaussian isoperimetric inequality


Barchiesi, Marco; Brancolini, Alessio; Julin, Vesa. Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality. Ann. Probab. 45 (2017), no. 2, 668--697. doi:10.1214/15-AOP1072.

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