Sharp bounds on the half-space two-point function for high-dimensional Bernoulli percolation

Abstract

We consider Bernoulli percolation on ${\mathbb{Z}}^d$ with $d>6$. We prove an up-to-constant estimate for the critical two-point function restricted to a half-space. This completes previous results of Chatterjee and Hanson (Commun. Pure Appl. Math., 2021), and Chatterjee, Hanson, and Sosoe (Commun. Math. Phys., 2023), and solves a question asked by Hutchcroft, Michta, and Slade (Ann. Probab., 2023).

16 pages, 2 figures. Accepted version, to appear in Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques