A Guide to First-Passage Processes

By Sidney Redner

Book Overview

First-passage properties underlie a wide range of stochastic processes, such as diffusion-limited growth, neuron firing, and the triggering of stock options. This book provides a unified presentation of first-passage processes, which highlights its interrelations with electrostatics and the resulting powerful consequences. The author begins with a modern presentation of fundamental theory including the connection between the occupation and first-passage probabilities of a random walk, and the connection to electrostatics and current flows in resistor networks. The consequences of this theory are then developed for simple, illustrative geometries including the finite and semi-infinite intervals, fractal networks, spherical geometries and the wedge. Various applications are presented including neuron dynamics, self-organized criticality, diffusion-limited aggregation, the dynamics of spin systems, and the kinetics of diffusion-controlled reactions. Examples discussed include neuron dynamics, self-organized criticality, kinetics of spin systems, and stochastic resonance.

• Format: Paperback
• Language: English
• ISBN: 0521036917
• ISBN13: 9780521036917
• Release Date: June 2007
• Publisher: Cambridge University Press
• Length: 328 Pages
• Weight: 1.26 lbs.
• Dimensions: 0.7" x 6.0" x 9.0"