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 $d>4$. 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 $d>6$.

arXiv comment31 pages, 5 figures. Accepted version, to appear in Probability Theory and Related Fields