The Annals of Probability

Polymers as Self-Avoiding Walks

Karl F. Freed

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Abstract

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.

Article information

Source
Ann. Probab., Volume 9, Number 4 (1981), 537-554.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994359

Digital Object Identifier
doi:10.1214/aop/1176994359

Mathematical Reviews number (MathSciNet)
MR624681

Zentralblatt MATH identifier
0468.60097

JSTOR
links.jstor.org

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60J65: Brownian motion [See also 58J65]

Keywords
Self-avoiding walks scaling theory Wiener integrals Gaussian random fields

Citation

Freed, Karl F. Polymers as Self-Avoiding Walks. Ann. Probab. 9 (1981), no. 4, 537--554. doi:10.1214/aop/1176994359. https://projecteuclid.org/euclid.aop/1176994359


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