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arXiv · 1608.07990

Robustness of the Gaussian concentration inequality and the Brunn-Minkowski inequality

Marco Barchiesi·Vesa Julin
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Abstract

We provide a sharp quantitative version of the Gaussian concentration inequality: for every $r>0$, the difference between the measure of the $r$-enlargement of a given set and the $r$-enlargement of a half-space controls the square of the measure of the symmetric difference between the set and a suitable half-space. We also prove a similar estimate in the Euclidean setting for the enlargement with a general convex set. This is equivalent to the stability of the Brunn-Minkowski inequality for the Minkowski sum between a convex set and a generic one.

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Marco Barchiesi, Vesa Julin. 2016-08-29. Robustness of the Gaussian concentration inequality and the Brunn-Minkowski inequality. https://doi.org/10.1007/s00526-017-1169-x

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