First steps in random walks : from tools to applications

By: J. KlafterContributor(s): I. M. SokolovMaterial type: TextTextPublication details: U.K.: Oxford University Press, [c2011]Description: 152 pISBN: 9780198754091LOC classification: QA274.73
Contents:
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 Lévy flights 8 Coupled CTRW and Lévy walks 9 Simple reactions: A + B → B 10 Random walks on percolation structures
Summary: 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. --- summary provided by publisher
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Item type Current library Collection Shelving location Call number Status Notes Date due Barcode Item holds
Book Book ICTS
Mathematic Rack No 5 QA274.73 (Browse shelf (Opens below)) Available Billno:IN 003 132; Billdate: 2017-12-04 00830
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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 Lévy flights
8 Coupled CTRW and Lévy walks
9 Simple reactions: A + B → B
10 Random walks on percolation structures

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. --- summary provided by publisher

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