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Synopsis
This is the first volume of a two-volume work devoted to probability theory in physics, physical chemistry and engineering. This volume provides an introduction to the problem of "random walk" and its applications. In its simplest form, the random walk describes the motion of an idealized drunkard and is a discrete analogue of the diffusion through a medium with traps, laser speckle and the conformations of polymers in dilute solution. Prior knowledge of probability theory is helpful, but not assumed.
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Review
Probabilists and statistical physicists will find it valuable to have it on their bookshelves (Rick Durrett, Cornell University, 1995)
Barry Hughes has written a classic and the field of random walks finally has a book worthy of its accomplishments. ... His approach has an even balance between mathematics and physics. ... In this truly scholarly work, Hughes goes so far as to correct the references used in the papers he cites. ... His presentation and analyses are careful and clear. ... Hughes has done a service to the community with this book and I wholeheartedly recommend it for students and researchers alike. (Fractals, vol.4, no.1, 1996.)
This whole volume is mathematically solid; the content of it is sufficiently rigorous and diverse to satisfy the needs of applied mathematicians, physicists, engineers and graduate students in related disciplines. (Mathematical Reviews)
...mathematicians will enjoy reading this book and [will] benefit greatly from this reading. (Metrika, vol.46(3), 1997)
This is the book on random walks.[]Every attempt has been made to make the book accessible to physicists and chemists with interests in its area, without in any way sacrificing mathematical rigour. Both volumes are clearly essential purchases for serious reference libraries in probability theory. (Journal of the Royal Statistical Society, Series A, vol.159, part 3, October 1996)
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