The self-avoiding walk Neal Madras, Gordon Slade

Format:

Book

Author/Creator:

Madras, Neal Noah, 1957-

Contributor:

Slade, G. (Gordon)

Series:

Modern Birkhäuser classics

Language:

English

Subjects (All):

Self-avoiding walks (Mathematics).

Mathematics.

applied mathematics.

mathematics.

Medical Subjects:

Mathematics.

Physical Description:

1 online resource

Place of Publication:

New York Birkhäuser ©2013

Language Note:

English

System Details:

text file

PDF

Summary:

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. TheSelf-Avoiding Walkprovides the firstunified 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 bookinclude: 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

Contents:

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

Notes:

Includes bibliographical references and index

Print version record

Other Format:

Print version Madras, Neal. Self-avoiding walk

ISBN:

9781461460251

1461460255

1461460247

9781461460244

OCLC:

820204654

Access Restriction:

Restricted for use by site license