Random Walks and Random Environments: Volume 2: Random Environments

ISBN-13: 9780198537892 / Angielski

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Opis

This is the second volume of a two-volume work devoted to probability theory in physical chemistry, and engineering. Rather than dealing explicitly with the idea of an ongoing random walk, with each chaotic step taking place at fixed time intervals, this volume addresses random environments-- models in which the disorder is frozen in space. It begins with an introduction to the geometry of random environments, emphasizing Bernoulli percolation models. The scope of the investigation then widens as we ask how structural disorder affects the transport process. The final chapters confront the interplay of two different forms of randomness; spatial randomness frozen into the environment and temporal randomness associated with the choices for next steps made by a random walker. The book ends with a discussion of "the ant in the labyrinth" problems and an extensive bibliography that, along with the rest of the material, will be of value to researchers in physics, mathematics, and chemical engineering.

Recenzje

... the author has successfully illuminated these major areas which are of critical importance to mathematics and physics. Both areas are characterised by significant mathematical theory which contains many beautiful results, wide ranging physical applicability and a vast scientific literature. Undoubtedly, the painstaking careful exposition of these important areas will be of considerable benefit to these involved in the mathematical modelling of random physical phenomena. Barry Hughes must again be congratulated for his marvellous exposition.