Borel type bounds for the self-avoiding walk connective constant

TL;DR

This paper establishes Borel type bounds for the asymptotic expansion of the self-avoiding walk connective constant on ^d, providing evidence that the expansion is Borel summable, which is significant for understanding its analytic properties.

Contribution

It proves Borel type bounds for the asymptotic expansion of the connective constant, supporting the conjecture of Borel summability.

Findings

Asymptotic expansion satisfies Borel type bounds

Supports conjecture of Borel summability of the expansion

Provides mathematical foundation for analytic continuation of the expansion

Abstract

Let $\mu$ be the self-avoiding walk connective constant on $\ZZ^d$. We show that the asymptotic expansion for $\beta_c=1/\mu$ in powers of $1/(2d)$ satisfies Borel type bounds. This supports the conjecture that the expansion is Borel summable.