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.