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

Stochastic processes.

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The book contains review articles on recent advances in first-passage phenomena and applications contributed by leading international experts. It is intended for graduate students and researchers who are interested in learning about this intriguing and important topic. Sample Chapter(s). Chapter 1: Arrival Statistics and Exploration Properties of Mortal Walkers (290 KB). Contents: Arrival Statistics and Exploration Properties of Mortal Walkers (S B Yuste et al.); First-Passage of a Randomly Accelerated Particle (T Burkhardt); First-Passage Problems in Anomalous Diffusion (A Rosso and A Zoia);

Statistical mechanics --- Stochastic processes --- Random walks (Mathematics) --- Additive process (Probability theory) --- Random walk process (Mathematics) --- Walks, Random (Mathematics) --- Random processes --- Probabilities --- Mechanics --- Mechanics, Analytic --- Quantum statistics --- Statistical physics --- Thermodynamics --- Study and teaching (Graduate)