The Self-Avoiding Walk [electronic resource] / by Neal Madras, Gordon Slade.

Preface.- Introduction -- Scaling, polymersand spins -- Some combinatorial bounds -- Decay of the two-point function -- The lace expansion -- Above four dimensions -- Pattern theorems -- Polygons, slabs, bridgesand knots -- Analysis of Monte Carlo methods -- Related Topics -- Random walk -- Proof of the renewal theorem -- Tables of exact enumerations -- Bibliography -- Notation -- Index..

The self-avoiding walk is a mathematical model that has important applications in statistical mechanics and polymer science. In spite of its simple definitiona path on a lattice that does not visit the same site more than onceit 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 Kestens 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.

ZDB-2-SMA