The Annals of Probability

The Scaling Limit of Self-Avoiding Random Walk in High Dimensions

Gordon Slade

Full-text: Open access

Abstract

The Brydges-Spencer lace expansion is used to prove that the scaling limit of the finite-dimensional distributions of self-avoiding random walk in the $d$-dimensional cubic lattice $\mathbb{Z}^d$ is Gaussian, if $d$ is sufficiently large. It is also shown that the critical exponent $\gamma$ for the number of self-avoiding walks is equal to 1, if $d$ is sufficiently large.

Article information

Source
Ann. Probab., Volume 17, Number 1 (1989), 91-107.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991496

Digital Object Identifier
doi:10.1214/aop/1176991496

Mathematical Reviews number (MathSciNet)
MR972773

Zentralblatt MATH identifier
0664.60069

JSTOR
links.jstor.org

Subjects
Primary: 82A67
Secondary: 60J15

Keywords
Self-avoiding random walk scaling limit lace expansion Brownian motion lattice models

Citation

Slade, Gordon. The Scaling Limit of Self-Avoiding Random Walk in High Dimensions. Ann. Probab. 17 (1989), no. 1, 91--107. doi:10.1214/aop/1176991496. https://projecteuclid.org/euclid.aop/1176991496


Export citation