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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 Zd\mathbb Z^d with d>6d>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).

Keywords

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

R2 v1 2026-07-01T08:25:45.886Z