3 problems

The edge-negative association conjecture. For every such graph $G$, the random forest $\Phi$ is edge-negatively associated. This is a longstanding problem concerning negative depen…

Update-stable zero-one conjecture. For every update-stable Borel set $\mathscr A\subseteq \{0,1\}^E$, the probability that $\mathfrak F$ belongs to $\mathscr A$ is either zero or o…

Let $G=(U,A)$ be a weighted digraph, let $K_p$ be the complete graph with vertex set $[p]$, and let $H=G\times K_p$ be their Cartesian product. A rooted forest of $H$ has a $G$-pro…