A Guide to First-Passage Processes

This book was published by Cambridge University Press in August 2001. The cover illustration, along with a short description from the inside cover of the book, is given below. It is meant to illustrate first-passage in a finite interval where death awaits at one boundary and a restaurant date awaits at the other.

List of errata; regrettably still growing and last updated December 11, 2011. If you find additional errors, please let me know.

Short list of exercises (updated Jan. 25 2003).

Some book reviews:
by Alan Bray (Journal of Statistical Physics, February 2002).
by Robert Dorfman (American Journal of Physics, November 2002).
by Paolo Laureti (Econophysics Forum, November 2002).

View the table of contents (ps format file).

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 provide a unified presentation of first-passage processes, which highlights its interrelations with electrostatics and the resulting powerful consequences. The goal of this book is to help those with modest background learn essential results quickly.

The author begins with a modern presentation of fundamental theory, including the connection between the occupation and first-passage probabilities of random walk and the connection to electrostatics and current flows in resistor networks. The consequence of this theory are then developed for simple, illustrative geometries including finite and semi-infinite intervals, fractal networks, spherical geometries, and the wedge. Various applications are presented including neuron dynamics, self-organized criticality, stochastic resonance, diffusion-limited aggregation, the dynamics of spin systems, and the kinetics of diffusion-controlled reactions.

First passage processes provide an appealing way for graduate students and research in physics, chemistry, theoretical biology, electrical engineering, chemical engineering, operations research, and finance to understand all of these systems.

Sidney Redner <redner@bu.edu>
Last modified: Mon Nov 8 22:09:29 EST 2004