Non-perturbative finite connectivities in supercritical Bernoulli percolation on ${\mathbb{Z}}^d$ with $d\ge 3$

Yacine Aoun, Kamil Khettabi

We solve a longstanding problem in Bernoulli percolation: we derive sharp Ornstein--Zernike asymptotics for the probability that two distant points are connected by a finite cluste…