Exponential tail of subcritical cluster size
= Exponential tail of subcritical cluster size
For independent <bond percolation> on $\mathbb Z^d$ below the <percolation critical probability>, there are $K,c>0$ such that $\mathbb P_p(|C(x)|\geq n)\leq Ke^{-cn}$, uniformly in $x$. This concerns the number of vertices in a <percolation cluster>, a stronger conclusion than decay of its radius alone.