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Self-avoiding walks. (English) Zbl 0795.60065
Self-avoiding walks are discrete paths without self-intersections, and play an important role in polymer science and statistical mechanics. This introductory review paper discusses the basic properties of self-avoiding walks on the integer lattice \(\mathbb{Z}^ d\), with emphasis on the asymptotic behaviour of the number of \(n\)-step self-avoiding walks and of the mean-square displacement. The critical exponents governing this asymptotic behaviour are described. Monte Carlo methods for analyzing self-avoiding walks are discussed. Lattice trees, lattice animals and percolation are briefly mentioned.
Reviewer: G.Slade (Hamilton)

MSC:
60G50 Sums of independent random variables; random walks
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
82D60 Statistical mechanical studies of polymers
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