First steps in random walks
Subtitle: from tools to applications
By: J. Klafter, I.M. Sokolov
Contributors: Sokolov, Igor M., 1958-
Publisher: Oxford University Press, USA; Oxford University Press
Published: 2011
Place of publication: Oxford; New York
Language: eng
Number of pages: 256
ISBN-13: 9780199234868
Subjects: Random walks (Mathematics); MATHEMATICS / Applied; MATHEMATICS / Discrete Mathematics; SCIENCE / Physics
Description: "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 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 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"--
Table of contents: title: Machine generated contents note:; title: 1. Characteristic Functions; title: 2. Generating Functions and Applications; title: 3. Continuous Time Random Walks; title: 4. CTRW and Aging Phenomena; title: 5. Master Equations; title: 6. Fractional Diffusion and Fokker-Planck Equations for Subdiffusion; title: 7. Levy Flights; title: 8. Coupled CTRW and Levy Walks; title: 9. Simple Reactions: A+B->B; title: 10. Random Walks on Percolation Structures.