upward

Random walks

Models

Fixed rates

Cicuta G M, Contedini M, Molinari L, Enumeration of simple random walks and tridiagonal matrices, JPA 35,1125 (2002)

Bass R, The Green's function for a finite linear chain, JMP 26, 3068 (1985)

General models

Jack R L, Sollich P, Duality between random trap and barrier models, JPA 41, 1 (2008)

Compte A, Bouchaud J-P, Localization in one-dimensional random random walks, JPA 31, 6113 (1998)

Zwanzig R, Non-Markoffian diffusion in a one-dimensional disordered lattice, JSP 28, 127 (1982)

Odagaki T, Lax M, ac hopping conductivity of a one-dimensional bond-percolation model, PRL 45, 847 (1980) – re

Alexander S, Bernasconi J, Orbach R, Spectral diffusion in a one-dimensional percolation model, PRB 17, 4311 (1978)

CTRW and related models

Balakrishnan V, van den Broeck C, Transport properties on a random comb, PA 217, 1 (1995)

Sinai model

Fontes L R G, Isopi M, Newman C M, Random walks with strongly inhomogeneous rates and singular diffusions: convergence, localization and aging in one dimension, math.PR/0009098

Kesten H, The limit distribution of Sinai's random walk in random environment, PA 138, 299 (1986)

Голосов А О, О предельных распределениях для случайного блуждания в критической одномерной случайной среде, УМН 41, 189 (1986)

Синай Я Г, Предельное поведение одномерного случайного блуждания в случайной среде, ТВП 27, 247 (1982)

Miscellaneous models

El-Shehawey M A, Absorption probabilities for a random walk between two partially absorbing boundaries: I, JPA 33, 9005 (2000)

Fisher D S, Le Doussal P, Monthus C, Random walks, reaction-diffusion, and nonequilibrium dynamics of spin chains in one-dimensional random environments, PRL 80, 3539 (1998)

Kehr K W, Mussawisade K, Wichmann T, Dieterich W, Rectification by hopping motion through nonsymmetric potentials with strong bias, PRE 56, R2351 (1997)

Godoy S, Espinosa F, One-dimensional quantum random walk for fermions and bosons, PRE 52, 3381 (1995)

Methods

Kawasaki M, The real-space renormalization group applied to diffusion in inhomogeneous media, cond-mat/0212613

Koza Z, Diffusion coefficient and drift velocity in periodic media, PA 285, 176 (2000)

Kehr K W, Murthy K P N, Ambaye H, Connection between dispersive transport and statistics of extreme events, PA 253, 9 (1998)

Guyer R A, Diffusion on a one-dimensional disordered lattice: A renormalization-group approach, PRA 29, 2114 (1984)

Stephen M J, Kariotis R, Diffusion in a one-dimensional disordered system, PRB 26, 2917 (1982) – replica

Miscellaneous

Gut A, Stopped random walks: limit theorems and applications (Springer, 1988)