Gaussian concentration inequality
= Gaussian concentration inequality
{c}
A Lipschitz function of a Gaussian vector has sub-Gaussian deviations from its mean, with scale controlled by the covariance operator and the Lipschitz constant. In particular, if the covariance operator norm is at most one and $f$ is one-Lipschitz, then universal constants $c,C>0$ give
$$
\mathbb P(f(X)>\mathbb Ef(X)+u)\leq C e^{-cu^2}.
$$