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An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions $d>6$
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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 $d>4$.
Forward citations
Cited by 3 Pith papers
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In the regime d > min{6, 3alpha}, critical long-range percolation clusters have an n^{-1/2} volume tail and integrated superprocess scaling limits, switching from super-Levy (alpha < 2) to super-Brownian (alpha >= 2);...
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Critical long-range percolation III: The upper critical dimension
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