An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions $d>6$

Hugo Duminil-Copin; Romain Panis

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arXiv · 2410.03647

An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions $d>6$

Hugo Duminil-Copin·Romain Panis

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Abstract

This article proposes a new way of deriving mean-field exponents for sufficiently spread-out Bernoulli percolation in dimensions $d>6$. We obtain an upper bound for the full-space and half-space two-point functions in the critical and near-critical regimes. In a companion paper, we apply a similar analysis to the study of the weakly self-avoiding walk model in dimensions $d>4$.

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Hugo Duminil-Copin, Romain Panis. 2024-10-04. An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions $d>6$. https://arxiv.org/abs/2410.03647

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