The <percolation probability> and <percolation critical probability> are
$$
\theta(p)=\mathbb P_p(0\leftrightarrow\infty),
\qquad
p_c=\inf\{p:\theta(p)>0\}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 204 / 2 / b / Solution

{title2=$\theta(p)$}

The percolation probability $\theta(p)$ is the probability that a specified root belongs to an infinite open cluster at parameter $p$.


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