Subcritical scaling of the two-point function in high-dimensional percolation
We study the scaling of the one-arm exponent in near-critical but subcritical percolation in high-dimensional percolation, extending a famous result of Kozma and Nachmias at the critical point. As a key tool, we derive a sharpening of existing half-plane two-point function bounds. As a by-product we also obtain the exact tail behavior for several quantities of interest in the model, including the cluster tail volume and chemical distances within clusters.
This is joint work with Shirshendu Chatterjee and Jack Hanson.