First Steps in Random Walks: From Tools to Applications

ISBN : 9780198754091

Joseph Klafter; I. M. Sokolov
160 Pages
181 x 247 mm
Pub date
Nov 2015
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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.


1. Characteristic Functions
2. Generating Functions and Applications
3. Continuous Time Random Walks
4. CTRW and Aging Phenomena
5. Master Equations
6. Fractional Diffusion and Fokker-Planck Equations for Subdiffusion
7. Levy Flights
8. Coupled CTRW and Levy Walks
9. Simple Reactions: A+B->B
10. Random Walks on Percolation Structures

About the author: 

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

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