$๐_{๐ผ}$-estimates for marginals of log-concave probability measures
$๐_{๐ผ}$-estimates for marginals of log-concave probability measures
We show that a random marginal $\pi _F(\mu )$ of an isotropic log-concave probability measure $\mu$ on $\mathbb R^n$ exhibits better $\psi _{\alpha }$-behavior. For a natural variant $\psi _{\alpha }^{\prime }$ of the standard $\psi _{\alpha }$-norm we show the following: [(i)] If $k\leq \sqrt {n}$, then for a โฆ