11 problems

Let $A_n(x)$ be an $n\times n$ random matrix whose entries are independent copies of a discrete random variable $x$. A discrete random matrix can be singular because it contains a…

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 $\mathbb{N}$.…

Studený's two-antecedent completeness conjecture. The semigraphoid axioms are complete for those inference rules of discrete conditional independence that have at most two antecede…

Pearl–Paz completeness conjecture. The semigraphoid axioms are complete for the theory of discrete conditional-independence structures.

Let $X_1,\ldots,X_n$ be independent random variables taking values in $\{0,1,\ldots,r\}$, and let … For $X_1,\ldots,X_{n-1}$, consider the uniform distribution on $\{0,r\}$. For…

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

Robinson's conjecture. Strong log-concavity implies log-submodularity for any generating polynomial $g_p$.