The one-arm exponent for mean-field long-range percolation

Tim Hulshof

Consider a long-range percolation model on ${\mathbb{Z}}^d$ where the probability that an edge $\{x,y\}\in {\mathbb{Z}}^d\times {\mathbb{Z}}^d$ is open is proportional to $\|x-y\|_2^{-…