Subcritical scaling of the two-point function in high-dimensional percolation

Mon October 4th 2021, 4:00pm
Sequoia 200
Phil Sosoe, Cornell University/MSRI

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.