Sharp bounds on the half-space two-point function for high-dimensional Bernoulli percolation
Probability
2026-03-09 v2 Mathematical Physics
math.MP
Abstract
We consider Bernoulli percolation on with . 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).
Cite
@article{arxiv.2512.13624,
title = {Sharp bounds on the half-space two-point function for high-dimensional Bernoulli percolation},
author = {Romain Panis and Bruno Schapira},
journal= {arXiv preprint arXiv:2512.13624},
year = {2026}
}
Comments
16 pages, 2 figures. Accepted version, to appear in Annales de l'Institut Henri Poincar\'e (B) Probabilit\'es et Statistiques