An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions $d>6$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911076526850048 |
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| author | Duminil-Copin, Hugo Panis, Romain |
| author_facet | Duminil-Copin, Hugo Panis, Romain |
| contents | 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 $d>4$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_03647 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions $d>6$ Duminil-Copin, Hugo Panis, Romain Probability Mathematical Physics 60K35, 82B27, 82B41 60K35, 82B27, 82B41, 82B43 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 $d>4$. |
| title | An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions $d>6$ |
| topic | Probability Mathematical Physics 60K35, 82B27, 82B41 60K35, 82B27, 82B41, 82B43 |
| url | https://arxiv.org/abs/2410.03647 |