The Self-Avoiding Walk (Probability and Its Applications) - Hardcover

Madras, Neal; Slade, Gordon

Hardcover

ISBN 10: 0817635890 ISBN 13: 9780817635893

Publisher: Birkhauser, 1992

Synopsis

The self-avoiding walk is a mathematical model with important applications in statistical mechanics and polymer science. This text provides a unified account of the rigorous results for the self-avoiding walk, focusing on its critical behaviour. Topics discussed include: the lace explosion 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; an 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; and the role of the self-avoiding walk in physical and chemical applications.

About this title

Review

"An excellent introduction for graduate students and professional probabilists... The best place to find a self-contained exposition of lace expansion."

―Bulletin of the AMS

"As a carefully written and carefully referenced exposition of an intriguing topic...this monograph is strongly recommended."

―Monatshefte Mathematik

"In this book, the reader will find basically everything there is to know about rigorous mathematical results on self-avoiding walks... It is nicely written and should be read by mathematical physicists and probabilists interested in applications to natural sciences."

―Belgian Mathematical Society

"This is the first book on self-avoiding random walk and a very good one."

―SIAM Review

"An excellent book that should be on the shelf of anyone doing work at the intersection of probability and critical phenomena... The best results about the SAW can still be found here."

--Annals of Probability

Edition details

• Publisher: Birkhauser
• Publication date: 1992
• Language: English
• ISBN 10: 0817635890
• ISBN 13: 9780817635893
• Binding: Hardcover