Upper bounds for the connective constant of weighted self-avoiding walks

Abstract: Building on an earlier work by Alm, we consider a model of weighted self-avoiding walks on a generic lattice and develop a systematic method for deriving upper bounds on the corresponding weighted connective constant. These bounds are obtained as the dominant eigenvalues of certain matrices and provide detailed information about the domain of convergence of the model's multivariate generating function. We discuss potential applications of this framework to developing Peierls-type estimates for contour models in statistical physics with anisotropic weights, generalizing a technique recently introduced by Fahrbach--Randall.