TY  - BOOK
AU  - J. Klafter
AU  - I. M. Sokolov
TI  - First steps in random walks: : from tools to applications
SN  - 9780198754091
AV  - QA274.73 
PY  - 2011///]
CY  - U.K.
PB  - Oxford University Press
N1  - 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
N2  - 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
ER  -