Random Walks and Random Environments: Volume 2: Random Environments

Hardcover | April 30, 1999

byBarry D. Hughes

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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, each chaotic step taking place at fixed time intervals, this volume addresses models in which thedisorder is frozen in space-random environments.The volume begins with a largely self-contained 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 twodifferent 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. It is supported by an extensive bibliography and verylittle prior knowledge is assumed.

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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, each chaotic step taking place at fixed time intervals, this volume addresses models in which thedisorder is frozen in space-random environments.The...

Barry D. Hughes is at University of Melbourne.

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Format:HardcoverDimensions:550 pages, 9.21 × 6.14 × 1.38 inPublished:April 30, 1999Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198537891

ISBN - 13:9780198537892

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Table of Contents

Notes on Text1. An Introduction to Percolation Theory2. Bernoulli Site Percolation3. Percolation Thresholds4. Critical Exponents in Percolation Theory5. Transport and Conduction6. Random Walk in a Random Environment7. The Ant in the LabyrinthErrata for the first Printing of Volume 1Additional References for Volume 1Index

Editorial Reviews

`...a valuable resource and reference for an area of great contemporary interest. It can be read either as a survey, by skipping the proofs, or with closer attention to the detailed arguments presented especially in the percolation chapters. Make sure that your library purchases a copy; but ifyou are an applied probabilist then you will also want a copy of your own, against the day when your applications lead you into this fascinating and challenging part of probability theory!'Journal of the Royal Statistical Society, Series A, vol.160, part 2, June 1997