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.