First Steps in Random Walks: From Tools to Applications
J. Klafter and I. M. Sokolov
Abstract
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 problem was posed by Louis Bachelier in his thesis devoted to the theory of financial speculations in 1900. Nowadays theory of random walks was proved useful in physics and chemistry (diffusion, reactions, mixing in flows), economics, biology (from animal spread to motion of subcellular structur ... More
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 problem was posed by Louis Bachelier in his thesis devoted to the theory of financial speculations in 1900. Nowadays theory of random walks was proved useful in physics and chemistry (diffusion, reactions, mixing in 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 superdiffusive transport processes as well. This book discusses main variants of the random walks and gives the most important mathematical tools for their theoretical description.
Keywords:
random walks,
continuous time random walks,
Levy walks and Levy flights,
fluctuation‐dominated kinetics,
percolation
Bibliographic Information
| Print publication date: 2011 |
Print ISBN-13: 9780199234868 |
| Published to Oxford Scholarship Online: December 2013 |
DOI:10.1093/acprof:oso/9780199234868.001.0001 |
Authors
Affiliations are at time of print publication.
J. Klafter, author
Heinemann Chair of Physical Chemistry, Tel Aviv University
I. M. Sokolov, author
Chair for Statistical Physics and Nonlinear Dynamics, Humboldt University, Berlin
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