## The Annals of Probability

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

### 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

**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