Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality
Marco Barchiesi, Alessio Brancolini, Vesa Julin
TL;DR
This paper presents a dimension-free, sharp quantitative estimate for the Gaussian isoperimetric inequality, improving understanding of how the inequality behaves with respect to asymmetry and mass.
Contribution
It provides a fully quantitative, dimension-independent version of the Gaussian isoperimetric inequality with optimal decay and dependence on mass.
Findings
Estimate is independent of dimension
Sharp decay rate with respect to asymmetry
Optimal dependence on the mass
Abstract
We provide a full quantitative version of the Gaussian isoperimetric inequality. Our estimate is independent of the dimension, sharp on the decay rate with respect to the asymmetry and with optimal dependence on the mass.
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