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January, 1989 The Scaling Limit of Self-Avoiding Random Walk in High Dimensions
Gordon Slade
Ann. Probab. 17(1): 91-107 (January, 1989). DOI: 10.1214/aop/1176991496


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.


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Gordon Slade. "The Scaling Limit of Self-Avoiding Random Walk in High Dimensions." Ann. Probab. 17 (1) 91 - 107, January, 1989.


Published: January, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0664.60069
MathSciNet: MR972773
Digital Object Identifier: 10.1214/aop/1176991496

Primary: 82A67
Secondary: 60J15

Keywords: Brownian motion , Lace expansion , lattice models , Scaling limit , Self-avoiding random walk

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 1 • January, 1989
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