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The Self-Avoiding Walk (Probability and its Applications) Book
The self-avoiding walk is a mathematical model that has important applications in statistical mechanics and polymer science. In spite of its simple definition - a lattice path that does not visit the same site more than once - it is difficult to analyze mathematically. This largely self-contained monograph provides the first unified account of the known rigorous results for the self-avoiding walk, with particular emphasis on its critical behavior. Its goals are to give an account of the current mathematical understanding of the model, to indicate some of the applications of the concept in physics and in chemistry, and to give an introduction to some of the nonrigorous methods used in those fields. Topics covered in the book include: the lace expansion and its application to the self-… read more...
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