Work

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

Year: 2025

Type: article

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.

Source: Journal of Physics A Mathematical and Theoretical

DOI: 10.1088/1751-8121/ae280e

Author: Qidong He

Institution: Rutgers, The State University of New Jersey

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

Funder: School of Graduate Studies, Rutgers, The State University of New Jersey