First Steps in Random Walks : From Tools to Applications - I. M. Sokolov

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First Steps in Random Walks

From Tools to Applications

By: I. M. Sokolov, J. Klafter

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Hardcover | 18 August 2011

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Hardcover
256 Pages

Dimensions(cm)
24.5 x 17.7 x 1.4

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$296.75

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The name "random walk" for a problem of a displacement of a point in a sequence of independent random steps was coined by Karl Pearson in 1905 in a question posed to readers of "Nature". The same year, a similar problem was formulated by Albert Einstein in one of his Annus Mirabilis works. Even earlier such a problem was posed by Louis Bachelier in his thesis devoted to the theory of financial speculations in 1900. Nowadays the theory of random walks has proved useful in physics and chemistry (diffusion, reactions, mixing flows), economics, biology (from animal spread to motion of subcellular structures) and in many other disciplines. The random walk approach serves not only as a model of simple diffusion but of many complex sub- and super-diffusive transport processes as well. This book discusses the main variants of random walks and gives the most important mathematical tools for their theoretical description.

Industry Reviews

`Most statistical physics books treat Brownian motion, but do not introduce the student to the many examples of anomalous diffusion. This is the void the Klafter-Sokolov book fills, to bring the student into contact with modern work on random walks with a unified approach. The power here is that straightforward mathematics can be employed to tackle a rich selection of problems in anomalous diffusion. One does not need to introduce many different techniques, but to successively generalize one method and apply it to topics in physics, chemistry, and biology. ' Michael Shlesinger, Office of Naval Research, USA `Klafter and Sokolov give us a systematic introduction to the mathematics of random walks, ranging from simple one-dimensional walks through Lévy flights to walks on percolation structures and fractals. "First Steps " should be required reading for physicists, theoretical chemists and biologists, and applied mathematicians interested in stochastic processes. ' Robert C. Hilborn, The University of Texas at Dallas, USA

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