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The Self-Avoiding Walk

The Self-Avoiding Walk
Catalogue Information
Field name Details
Dewey Class 519.2 (DDC 23)
Title The Self-Avoiding Walk (EB) / by Neal Madras, Gordon Slade.
Author Madras, Neal
Added Personal Name Slade, Gordon author.
Other name(s) SpringerLink (Online service)
Publication New York, NY : Birkhäuser
, 2013.
Physical Details XVI, 427 p. : online resource.
Series Modern Birkhäuser classics
ISBN 9781461460251
Summary Note The self-avoiding walk is a mathematical model that has important applications in statistical mechanics and polymer science. In spite of its simple definitionâa path on a lattice that does not visit the same site more than onceâit is difficult to analyze mathematically. The Self-Avoiding Walk 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's include: the lace expansion and its application to the self-avoiding walk in more than four dimensions where most issues are now resolved; an introduction to the nonrigorous scaling theory; classical work of Hammersley and others; a new exposition of Kestenâs pattern theorem and its consequences; a discussion of the decay of the two-point function and its relation to probabilistic renewal theory; analysis of Monte Carlo methods that have been used to study the self-avoiding walk; the role of the self-avoiding walk in physical and chemical applications. Methods from combinatorics, probability theory, analysis, and mathematical physics play important roles. The book is highly accessible to both professionals and graduate students in mathematics, physics, and chemistry.:
Contents note Preface.-  Introduction -- Scaling, polymers' and spins -- Some combinatorial bounds -- Decay of the two-point function -- The lace expansion -- Above four dimensions -- Pattern theorems -- Polygons, slabs, bridges' and knots -- Analysis of Monte Carlo methods -- Related Topics -- Random walk -- Proof of the renewal theorem -- Tables of exact enumerations -- Bibliography -- Notation -- Index. .
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