A Guide to First-Passage Processes

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.

Sid Redner is a condensed-matter theorist whose research focuses on non-equilibrium statistical physics and its applications. Dr Redner has been on the physics faculty at Boston University since 1978 and has been a full professor since 1989. He has published 230 research articles and is the author of A Kinetic View of Statistical Physics with P. L. Krapivsky and E. Ben-Naim (Cambridge University Press, 2010). Dr Redner is a Fellow of the American Physical Society and was a visiting scientist at Schlumberger Research in 1984–1985, the Ulam Scholar at Los Alamos National Laboratory in 2004–2005 and a visiting professor at the Universite Paul Sabatier (Toulouse) and Universite Pierre et Marie Curie (Paris) in 2008.