Random Walks and Random Environments Volume 1 Random Walks [Hardcover]

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.

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

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 applilãº