First Steps in Random Walks From Tools to Applications

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.

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-agt,B. 10. Random Walks on Percolation Structures.

Professor Klafter is a Fellow of the American Physical Society, and has won the Alexander von Humboldt Foundation Prize, the Weizmann Prize for Sciences, the Rothschild Prize in Chemistry, and the Israel Chemical Society Prize. He also holds an honorary doctorate from Wroclaw University of Technology in Poland. He has been the President of Tel Aviv University since 2009. Professor Klafter has published close to 400 scientific articles and edited 18 books. He is a member of the editorial boards of six scientific journals, and has been a member of the scientific committee of dozens of conferences. Professsor Sokolov has taught at the P.N. Lebedev Physical Institute of the Academy of Sciences of the USSR, the University of Bayreth (Germany), the University of Freiburg (Germany). Professor Sokolov currently holds the Chair for Statistical Physics and Nonlinear Dynamics at the Institute of Physics at Humboldt University in Berlin. He is the author of more than 200 publications in statistical physics as well as physical chemistry of condensed and soft matter, especially problems regarding disordered systems and polymers.