2 problems

Let $(X,Y)$ be a symmetric $\kappa$-concave random vector in $\mathbb{R}^2$, and suppose that $X$ and $Y$ have equal $p$-Rényi entropy. Convexity conjecture for Rényi entropy. The…

Recall that a probability measure on $\mathbb{R}^n$ is $\kappa$-concave if it satisfies the Brunn–Minkowski-type inequality associated with $\kappa$; a random vector is $\kappa$-co…