Consider a graph G and let each edge be present (open) with probability p independently of each other. Given vertices s, a, t and b, consider the event {s ↔ a} that there is a path between s and a, and the event {t ↔ b} that there is a path between t and b. It is a classical fact, called Harris inequality, that these two events are positively correlated, i.e. if we know that one is...