Work

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

Year: 2025

Type: article

Abstract: 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].

Source: Probability Theory and Related Fields

DOI: 10.1007/s00440-025-01415-3

Authors: Hugo Duminil-Copin, Romain Panis

Institutions: University of Geneva, Institut des Hautes Études Scientifiques, Institut Camille Jordan

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090