6 problems

Representability conjecture. Every maxoid is representable as the conditional-independence structure of a positive discrete distribution.

Asymptotic counting conjecture. The number of compositional graphoids which are representable by $n$ discrete random variables is asymptotically

Ollivier-Ricci curvature and LSI. There exists a universal constant $c<\infty$ such that whenever the Ollivier-Ricci curvature $\tilde{\kappa}$ is positive, we have

Fix an integer $k\geq2$. In the discrete stick-fragmentation process, break each stick into $k$ pieces by choosing $k-1$ cut points recursively according to the uniform distributio…

Let $k\geq 2$, let $(p_1,p_2,\ldots,p_{k-1})$ be a permutation of $\{1/2,1/2^2,\ldots,1/2^{k-1}\}$, and define the probability measure … on $\mathbb{R}$, supported on $\mathbb{N}$.…

Strengthened varentropy conjecture. The function $K$ is log-concave: $\log K(t)$ is concave on $(-\gamma,+\infty)$.