A Gaussian small deviation inequality for convex functions

Grigoris Paouris, Petros Valettas

Let $Z$ be an $n$-dimensional Gaussian vector and let $f:{\mathbb{R}}^n\to \mathbb{R}$ be a convex function. We show that: $$\mathbb P \left( f(Z) \leq \mathbb E f(Z) -t\sqrt{ {\rm V…