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

Hugo Duminil-Copin; Romain Panis

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

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arxiv 2410.03647 v2 pith:NHZCHW3R submitted 2024-10-04 math.PR math-phmath.MP

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

Hugo Duminil-Copin , Romain Panis This is my paper

classification math.PR math-phmath.MP

keywords dimensionsbernoullimean-fieldpercolationspread-outalternativeanalysisapply

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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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