Dimitris-Marios Liakopoulos

Moment comparisons, Sudakov inequalities and entropy of centroid bodies

Let $X$ be an isotropic log-concave random vector in $\mathbb{R}^n$ and let $G$ be standard Gaussian. Starting from the first moment comparison for gauges, we derive corresponding estimates at arbitrary moment orders. For every gauge $\phi$ and every $q\geqslant 1$, $$ \|\phi(G)\|_q\leqslant C\sqrt{\ln(en)+q}\,\|\phi(X...