An alternative approach for the mean-field behaviour of weakly self-avoiding walks in dimensions $$d>4$$
Abstract This article proposes a new way of deriving mean-field exponents for the weakly self-avoiding walk model in dimensions $$d>4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>></mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> . 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 $$d>6$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>></mml:mo> <mml:mn>6</mml:mn> </mml:mrow> </mml:math> [10].
Authors
- Romain Panis (ORCID: https://orcid.org/0009-0001-4604-8398)
- Hugo Duminil‐Copin (ORCID: https://orcid.org/0000-0002-7609-2816)
Institutions
- Université Claude Bernard Lyon 1 (FR)
- University of Geneva (CH)
- Institut Camille Jordan (FR)
- Institut des Hautes Études Scientifiques (FR)
Publication Details
- Journal
- Probability Theory and Related Fields
- Published
- 2025-10-08
- DOI
- https://doi.org/10.1007/s00440-025-01415-3
- Citations
- 1
- Primary Topic
- Theoretical and Computational Physics
- Type
- article
- Field-Weighted Citation Impact
- 1.26
Funders
- National Science Foundation
- National Centres of Competence in Research SwissMAP
- European Commission
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
- Université de Genève