Open Access
Translator Disclaimer
August, 1981 Polymers as Self-Avoiding Walks
Karl F. Freed
Ann. Probab. 9(4): 537-554 (August, 1981). DOI: 10.1214/aop/1176994359


A brief overview is presented of the relation of the properties of real polymers to the problem of self-avoiding random walks. The self-consistent field method is discussed wherein the non-Markovian continuous self-avoiding polymer is replaced by a self-consistent Markovian approximation. An outline is presented of the method of solution of the resultant nonlinear integrodifferential equations. A description is also presented of the scaling theories which provide a means for deducing some exponents in the asymptotic dependence of walk properties on the length of the walk in the limit of infinite length walks.


Download Citation

Karl F. Freed. "Polymers as Self-Avoiding Walks." Ann. Probab. 9 (4) 537 - 554, August, 1981.


Published: August, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0468.60097
MathSciNet: MR624681
Digital Object Identifier: 10.1214/aop/1176994359

Primary: 60K35
Secondary: 60J65

Keywords: Gaussian random fields , scaling theory , self-avoiding walks , Wiener integrals

Rights: Copyright © 1981 Institute of Mathematical Statistics


Vol.9 • No. 4 • August, 1981
Back to Top