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<p>This article proposes a new way of deriving mean-field exponents for the weakly self-avoiding walk model in dimensions <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(d&gt;4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>&gt;</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation>. 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 <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(d&gt;6\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>&gt;</mo> <mn>6</mn> </mrow> </math></EquationSource> </InlineEquation> [<CitationRef CitationID="CR10">10</CitationRef>].</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月8日

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  • Hugo Duminil-Copin,
  • Romain Panis

摘要

This article proposes a new way of deriving mean-field exponents for the weakly self-avoiding walk model in dimensions \(d>4\) 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 \(d>6\) d > 6 [10].