Markov chains and random walks

Random walk (general studies)

Rudnick J, Gaspari G, Elements of the random walk: An introduction for advanced students and researchers (CUP, 2004)

Redner S, A guide to first-passage processes (CUP, 2001)

Bazant M, Lecture notes on random walks (2001)

Ben-Avraham D, Havlin S, Diffusion and reactions in fractals and disordered systems (CUP, 2000)

Hughes B D, Random walks and random environments. Volume 1: Random walks (Clarendon Press, Oxford, 1995)

Hughes B D, Random walks and random environments. Volume 2: Random environments (Clarendon Press, Oxford, 1996)

Weiss G H, Aspects and applications of the random walk (North­Holland, Amsterdam, 1994)

Bouchaud J P, Georges A, Anomalous diffusion in disordered media: Statistical mechanics, models and physical applications, PR 195, 127 (1990)

Havlin S, Ben-Avraham D, Diffusion in disordered media, AP 36, 695 (1987)

Haus J W, Kehr K W, Diffusion in regular and disordered lattices, PR 150, 263 (1987)

Percolation (general studies)

Percolation threshold (Wikipedia)

Hunt A G, Percolation theory for flow in porous media, LNP 674 (Springer, 2005)

Ю Ю Тарасевич, Перколяция: теория, приложения, алгоритмы (УРСС, 2002)

Romer R A, Percolation, renormalization and the Quantum-Hall transition, cond-mat/0106004

Grimmett G R, Percolation, in Development of mathematics 1950-2000, ed Pier J-P, p 547 (Birkhauser, 2000)

Grimmett G R, Percolation (Springer, New York, 1999)

A Bain, The Percolation Phase Transition (Lecture Notes, 1999)

Stanley H E, Andrade Jr. J S, Havlin S, Makse H A, Suki B, Percolation phenomena: a broad-brush introduction with some recent applications to porous media, liquid water, and city growth, PA 266, 5 (1999)

Grimmett G R, Percolation and disordered system, LNM 1665, 153 (1997)

Stauffer D, Aharony A, Introduction to percolation theory (TF, 1994)

Кестен Х, Теория просачивания для математиков (Мир, 1986)

Соколов И М, Размерности и другие геометрические критические показатели в теории протекания, УФН 150, 221 (1986)

Essam J W, Percolation theory, RPP 43, 833 (1980)

Stauffer D, Scaling theory of percolation clusters, PR 54, 1 (1979)

Шкловский Б И, Эфрос А Л, Теория протекания и проводимость сильно неоднородных сред, УФН 117, 401 (1975)

Shante V K S, Kirkpatrick S, An introduction to percolation theory, AP 20, 325 (1971)

Domb C, Series expansions for ferromagnetic models, AP 19, 339 (1970)


Anomalous transport: Foundations and Applications, ed Radons G, Klages R, Sokolov I M (Wiley, 2008)

Sahimi M, Non-linear and non-local transport processes in heterogeneous media: from long-range correlated percolation to fracture and materials breakdown, PR 306, 213 (1998)

Anomalous diffusion: From basics to applications, ed A Pekalski, K Sznajd-Weron, LNP 519 (Springer, 1999)

Fractals and disordered systems, ed Bunde A, Havlin S (Springer, 1996)

Contemporary problems in statistical physics, ed Weiss G H (SIAM, Philadelphia, 1994)

Revesz P, Random walks of infinitely many particles (WSPC, 1994)

Montroll E W, Shlesinger M F, On the wonderful world of random walks, in Nonequilibrium Phenomena II, ed Montroll E W, Lebowitz J L, p 1 (Elsevier, 1984)