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arXiv · 2410.03649

An alternative approach for the mean-field behaviour of weakly self-avoiding walks in dimensions $d>4$

Hugo Duminil-Copin·Romain Panis
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Abstract

This article proposes a new way of deriving mean-field exponents for the weakly self-avoiding walk model in dimensions $d>4$. Among other results, we obtain up-to-constant estimates for the full-space and half-space two-point functions in the critical and near-critical regimes. A companion paper proposes a similar analysis for spread-out Bernoulli percolation in dimensions $d>6$.

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Hugo Duminil-Copin, Romain Panis. 2024-10-04. An alternative approach for the mean-field behaviour of weakly self-avoiding walks in dimensions $d>4$. https://arxiv.org/abs/2410.03649

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