Many phenomena of interest in stochastic processes are governed by, or can be regarded as, first passage events. Redner's book clarifies the above statement, providing a unified theory of first passage probability and its applications, with a modern perspective and various new results. In this respect it constitutes a precious complement to the classical monographs of Feller and Van Kampen. In fact the author gives a presentation of the fundamental theory of random walks, solving first passage problems by both direct approaches and developing an elegant electrostatic equivalence. Then he treats several classical and modern interdisciplinary applications, from statistical mechanics to biology and economics.
Redner's approach is always remarkably clear and it is often aimed to develop intuition. This way, for instance, the relation between avalanches in extremal dynamics driven systems and the first passage of a random walk in the semi infinite interval, is elucidated with abundance of illuminating examples. The book is explicitly intended for allowing those with a modest background to learn essential results quickly. This goal intrinsically places it on the border between the category of textbooks and that of reference books. The author's style, colloquial and concise, yet precise, is definitely appropriate for the purpose.
This review appeared in the Econophysics Form, November 2002.