The Self-Avoiding Walk

• Main Authors: Madras, Neal (Author), Slade, Gordon (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Birkhäuser, 2013.
• Series: Modern Birkhäuser Classics
• Subjects: Mathematics.; Mathematical physics.; Probabilities.; Combinatorics.; Probability Theory and Stochastic Processes.; Mathematical Applications in the Physical Sciences.; Mathematical Physics.

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 provid...

Table of Contents:

• 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. .