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The Self-Avoiding Walk

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Published by Springer New York, Imprint: Birkhäuser in New York, NY .
Written in English

Subjects:

  • Probability Theory and Stochastic Processes,
  • Mathematical physics,
  • Mathematical Applications in the Physical Sciences,
  • Mathematics,
  • Distribution (Probability theory),
  • Combinatorial analysis

Book details:

About the Edition

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 path on a lattice that does not visit the same site more than once—it 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 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 Kesten’s 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.​

Edition Notes

Statementby Neal Madras, Gordon Slade
SeriesModern Birkhäuser Classics
ContributionsSlade, Gordon, SpringerLink (Online service)
Classifications
LC ClassificationsQA273.A1-274.9, QA274-274.9
The Physical Object
Format[electronic resource] /
PaginationXVI, 427 p.
Number of Pages427
ID Numbers
Open LibraryOL27086974M
ISBN 109781461460251

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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 Author: Neal Madras. 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 path on a lattice that does not visit the same site more than once—it is difficult to analyze mathematically. 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 path on a lattice that does not visit the same site more than once—it is difficult to analyze mathematically. The Self-Avoiding. These and other important questions about the self-avoiding walk remain unsolved in the rigorous mathematical sense, although the physics and chemistry communities have reached consensus on the Read more.

A second goal of this book is to discuss some of the applications of the self-avoiding walk in physics and chemistry, and to describe some of the nonrigorous methods used in those fields. The model originated in chem istry several decades ago . Get this from a library! The self-avoiding walk. [Neal Noah Madras; Gordon Douglas Slade] -- A self-avoiding walk is a path on a lattice that does not visit the same site more than once. In spite of this simple definition, many of the most basic questions about this model are difficult to. The book begins with critical behaviour and its basic discussion in statistical mechanics models, and subsequently explores perturbative and non-perturbative analysis in the renormalisation group. Lastly it discusses the relation of these topics to the self-avoiding walk and supersymmetry. Book Title: The Self Avoiding Walk: Author: Neal Madras: Publisher: Springer Science & Business Media: Release Date: Pages: ISBN: Available Language: English, Spanish, And French: DOWNLOAD READ ONLINE. EBOOK SYNOPSIS: A self-avoiding walk is a path on a lattice that does not visit the same site more than once. In.

A self-avoiding walk is a path on a lattice that does not visit the same site more than once. In spite of this simple definition, many of the most basic questions about this model are difficult to resolve in a mathematically rigorous fashion. In particular, we do not know much about how far an n­. Download Citation | The self-avoiding walk. Reprint of the edition | The self-avoiding walk is a mathematical model that has important applications in statistical mechanics and polymer. Talk:Self-avoiding walk. Jump to navigation Jump to search. WikiProject Mathematics (Rated C-class, Mid-importance) The "pages=" of the reference of Flory's book is wrong. Page is the last Page! A citation to the whole book for this really specific statement is useless! Some pages part of the book should be specified.(Rated C-class, Mid-importance): . The self-avoiding walk, and lattice spin systems such as the φ⁴ model, are models of interest both in mathematics and in physics. Many of their important mathematical problems remain unsolved.