Percolation cluster-size tail exponent ($P_{p_c}(|C(0)|\ge s)=s^{-1/\delta +o(1)}$)

The exponent $\delta$ describes the tail of the critical cluster seen from a specified vertex of a graph. If the expected number of size-$s$ clusters per site scales as $s^{-\tau }$, weighting by cluster size gives $1/\delta =\tau -2$ when these scaling laws hold.