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March 2017 Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality
Marco Barchiesi, Alessio Brancolini, Vesa Julin
Ann. Probab. 45(2): 668-697 (March 2017). DOI: 10.1214/15-AOP1072

Abstract

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.

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Marco Barchiesi. Alessio Brancolini. Vesa Julin. "Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality." Ann. Probab. 45 (2) 668 - 697, March 2017. https://doi.org/10.1214/15-AOP1072

Information

Received: 1 April 2015; Revised: 1 October 2015; Published: March 2017
First available in Project Euclid: 31 March 2017

zbMATH: 1377.49050
MathSciNet: MR3630285
Digital Object Identifier: 10.1214/15-AOP1072

Subjects:
Primary: 49Q20
Secondary: 60E15

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 2 • March 2017
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