# On the tightness of Gaussian concentration for convex functions

@article{Valettas2019OnTT, title={On the tightness of Gaussian concentration for convex functions}, author={Petros Valettas}, journal={Journal d'Analyse Math{\'e}matique}, year={2019} }

The concentration of measure phenomenon in Gauss' space states that every $L$-Lipschitz map $f$ on $\mathbb R^n$ satisfies \[ \gamma_{n} \left(\{ x : | f(x) - M_{f} | \geqslant t \} \right) \leqslant 2 e^{
- \frac{t^2}{ 2L^2} }, \quad t>0, \] where $\gamma_{n} $ is the standard Gaussian measure on $\mathbb R^{n}$ and $M_{f}$ is a median of $f$. In this work, we provide necessary and sufficient conditions for when this inequality can be reversed, up to universal constants, in the case when $f…

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