Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 209 / 3 / e / Solution

The stochastic bounds from part (b) hold uniformly in every box. Passing to the increasing limit for the local increasing event $A$ givesThus the infinite-volume free random-cluster measure lies stochastically between Bernoulli bond percolation at parameters $p/(2-p)$ and $p$.