Random Walks and Random Environments

by Barry D. Hughes

Overview

This is the first of two volumes devoted to probability theory in physics, physical chemistry, and engineering, providing an introduction to the problem of the random walk and its applications. In its simplest form, the random walk describes the motion of an idealized drunkard and is a discreet analogy of the diffusion process. A thorough account is given of the theory of random walks on discreet spaces (lattices or networks) and in continuous spaces, including those processed with random waiting time between steps. Applications discussed include dielectric relaxation, charge transport in the xerographic process, turbulent dispersion, diffusion through a medium with traps, laser speckle and the conformations of polymers in dilute solution. Prior knowledge of probability theory would be helpful, but not assumed. An extensive bibliography concludes the book.

Product Details

ISBN-13:	9780198537885
Publisher:	Oxford University Press
Publication date:	05/18/1995
Edition description:	New Edition
Pages:	652
Product dimensions:	9.26(w) x 6.38(h) x 1.78(d)

About the Author

University of Melbourne

Table of Contents

1. Introduction
2. Random walks and random flights
3. Random Walks on a Lattice
4. Random walks in the continuum limit
5. Continuous-time random walks
6. Exploration and Trapping
7. The Self-Avoiding Walk
Appendices: Special Functions for Random Walk Problems; Mellin Transforms and Asymptotic Expansions; Green Functions for Lattice Walks

Editorial Reviews

"The author seems to have tracked down and catalogued every conceivable variation on the basic themes from the very theoretical to the very computational.... It contains information on a huge number of topics.... Probabilists and statistical physicists will find it valuable to have it on their bookshelves at home." —Rick Durrett, Cornell University

"Barry Hughes has written a classic and the field of random walks finally has a book worthy of its accomplishments." —Fractals

"This book contains an enormous amount of material about random walks in translationally invariant media in addition to an excellent bibliography of the research done in this general area up till 1994 with a slant toward physical applications. I recommend it as a scholarly and very competent piece of work, and certainly look forward to reading Volume 2, which is organized around the theme of transport in disorded media."—Journal of Statistical Physics

"This whole volume is mathematically solid; the content of it is sufficiently rigorous and diverse to satisfy the needs of applied mathematicians, physicists, engineers and graduate students in related disciplines. Due to the attractive topics as well as the informal and vivid style often used in the presentation and description of the challenging mathematical and physical problems, they will find this book a very readable one and will benefit a lot from it . . . . All in all, this book, written with the author's careful effort over many years, is a great pleasure to read."—Mathematical Reviews

"There is a rich class of discrete mathematical models . . . of profound importance both to probability and statistical physics. Hughes' ambitious pair of volumes . . . offers a wide-ranging introduction to two of the most fundamental of these models: random walk and percolation. . . . The mathematical treatment is careful . . . The style is down-to-earth, and the notation of physicists is generally preferred to that of mathematicians. The mathematical background required of the reader is not extensive. Long and complicated proofs are omitted, with clear references to the literature. These features will make Hughes' volumes particularly accessible to applied scientists. Historical references abound throughout . . . These two impressive volumes contain a wealth of material. They will serve as a useful introduction to newcomers to the field and as a valuable reference to researchers . . . whose work touches on random walks or percolation."—Bulletin of the American Mathematical Society

From the Publisher