2 problems

Let $f$ be an isotropic down-monotone logconcave function in $\mathbb{R}^m$, and let $X$ have density $f$. Let $1>p>0$. The conditional-coordinate-tail conjecture. There exists an…

Let $F$ be a distribution in the positive orthant with a down-monotone logconcave density. For each coordinate $e$, write ${\sf E}(X_e^2)=\sigma_e^2$, and let…