## The Annals of Probability

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

#### 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

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