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.
• Highlights first-passage processes; most books on probability theory and stochastic processes treat it as a subsidiary • The emphasis is on physical intuition and how to solve problems rather than on theory • A range of applications are presented as being part of first-passage processes
Preface; Errata; 1. First-passage fundamentals; 2. First passage in an interval; 3. Semi-infinite system; 4. Illustrations of first passage in simple geometries; 5. Fractal and nonfractal networks; 6. Systems with spherical symmetry; 7. Wedge domains; 8. Applications to simple reactions; References; Index.
'… this is unquestionably a valuable book, written at an accessible level for graduate students while providing a nice summary of the last century's - and notably the last two decades' - developments of these methods. I do not doubt that this will be a popular book; it fills a hole in the textbook/monograph literature that's needed filling for at least ten years. Moreover, the author's style is relaxed and crystal clear while maintaining mathematical precision and power.' Charles Doering, University of Michigan
'… to practitioners in the field of first-passage problems and to students entering the field … I can recommend it strongly … It is clearly written and the organisation and presentation of the material are excellent. It serves as a useful repository of standard and not-so-standard techniques which anyone working in the area of stochastic processes in general, and first-passage problems in particular, will want to have on their shelves.' Alan J. Bray, The Journal of Statistical Physics
'I found the author's style accessible and interesting.' Contemporary Physics