6 problems

Let $P$ and $Q$ be probability measures, let $V(P,Q)$ denote their total variation distance, and define … For $v$ in the relevant small-distance regime, Sixth-order surplus asympto…

Let $u>0$. Sixth-order logarithmic inequality. The following inequality should hold: … This would provide a pointwise sixth-order refinement of the second- and fourth-order bounds…

Generalization to $\phi$-divergences. The arguments developed to study higher moment measures should generalize to arbitrary $\phi$-divergences.

In minimax detection, hypotheses and action/uncertainty sets determine the class of admissible detectors, while an $f$-divergence is a statistical similarity measure used as a surr…

Two- and three-point sharpness conjecture. For the relevant values of $D_1$,

Let $A$ and $B$ be positive elements in a finite-dimensional $C^*$-algebra, and let $\Phi$ be a stochastic map. For a convex function $f$, write $S_f(A\|B)$ for the associated quan…