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.
Publié le : 1989-01-14
Classification:
Self-avoiding random walk,
scaling limit,
lace expansion,
Brownian motion,
lattice models,
82A67,
60J15
@article{1176991496,
author = {Slade, Gordon},
title = {The Scaling Limit of Self-Avoiding Random Walk in High Dimensions},
journal = {Ann. Probab.},
volume = {17},
number = {4},
year = {1989},
pages = { 91-107},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991496}
}
Slade, Gordon. The Scaling Limit of Self-Avoiding Random Walk in High Dimensions. Ann. Probab., Tome 17 (1989) no. 4, pp. 91-107. http://gdmltest.u-ga.fr/item/1176991496/