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

Abstract We introduce a method for computing upper bounds on the connective constant of weighted self-avoiding walks on a lattice, extending a framework developed by Alm for the unweighted case. To make our method readily applicable, we implement it in a publicly available software package. The upper bounds are obtained as the dominant eigenvalues of certain matrices and provide detailed information about the convergence of the model’s multivariate generating function. We also consider applications of our results to developing Peierls-type estimates for anisotropic contour models in statistical physics, generalizing a technique recently introduced by Fahrbach–Randall.