3 problems

Derivative-comparison conjecture. For $r\geq1$ and $\beta_c/2\leq\beta\leq\beta_c$,

Let $a$, $b$, and $c$ be vertices, and let $\mathbf{P}(ab\\|c)$, $\mathbf{P}(abc)$, $\mathbf{P}(ac)$, and $\mathbf{P}(bc)$ denote the corresponding bond-percolation event probabili…

Let $a$, $b$, and $c$ be vertices, and let $\mathbf{P}(ab\\|c)$, $\mathbf{P}(ac\\|b)$, $\mathbf{P}(abc)$, and $\mathbf{P}(a\\|b\\|c)$ denote the corresponding bond-percolation even…