The <van den Berg-Kesten inequality> says that for increasing cylinder events $A$ and $B$ under product bond percolation,
$$
\mathbb P_p(A\mathbin\square B)
\leq\mathbb P_p(A)\mathbb P_p(B),
$$
where $A\mathbin\square B$ is the event that $A$ and $B$ have disjoint finite witness edge sets.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 204 / 3 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-204/3/a/solution