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

Romain Panis; Bruno Schapira

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arXiv · 2512.13624

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

Romain Panis·Bruno Schapira

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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).

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Romain Panis, Bruno Schapira. 2025-12-15. Sharp bounds on the half-space two-point function for high-dimensional Bernoulli percolation. https://arxiv.org/abs/2512.13624

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