First Steps in Random Walks: From Tools to Applications

Paperback | December 5, 2015

byJ. Klafter, I. M. Sokolov

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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 ofsubcellular 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 mathematicaltools for their theoretical description.

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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 ...

J. Klafter is Heinemann Chair of Physical Chemistry at Tel Aviv University. I. M. Sokolov is Chair for Statistical Physics and Nonlinear Dynamics at Humboldt University, Berlin.

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Format:PaperbackDimensions:160 pages, 9.69 × 6.73 × 0.07 inPublished:December 5, 2015Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198754094

ISBN - 13:9780198754091

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Table of Contents

1. Characteristic Functions2. Generating Functions and Applications3. Continuous Time Random Walks4. CTRW and Aging Phenomena5. Master Equations6. Fractional Diffusion and Fokker-Planck Equations for Subdiffusion7. Levy Flights8. Coupled CTRW and Levy Walks9. Simple Reactions: A+B-B10. Random Walks on Percolation Structures

Editorial Reviews

"Klafter and Sokolov give us a systematic introduction to the mathematics of random walks, ranging from simple one-dimensional walks through Levy 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