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More About This Textbook
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.
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Table of Contents
Introduction
1. Random walks and random flights
2. Polya's Problem for a lattice walk
3. Random walks in the continuum limit
4. Continuous-time random walks
5. Exploration by a random walker
6. Self-avoiding walks
7. An introduction to percolation theory
8. Bernoulli site percolation
9. Percolation thresholds
10. Critical exponents in percolation theory
11. Transport and conduction in random systems A1: Special functions arising in random walk problems A2: Mellin transforms and asymptotic expansions A3: Green functions for lattice walks