upward

Random walks

Barlow M T, Diffusions on fractals, LNM 1690, 1 (1998)

Simple random walk

Knezevic M, Knezevic D, Spasojevic D, Statistics of equally weighted random paths on a class of self-similar structures, JPA 37, 1 (2004)

Kron B, Teufl E, Asymptotics of the transition probabilities of the simple random walk on self-similar graphs, math/0209143

Kron B, Green functions on self-similar graphs and bounds for the spectrum of the laplacian, math/0202172

Osada H, A family of diffusion processes on Sierpinski carpets, Probab Theory Related Fields 119, 275 (2001)

Essex C, Davison M, Schulzky C, Franz A, Hoffmann K H, The differential equation describing random walks on the Koch curve, JPA 34, 8397 (2001)

Seeger S, Franz A, Schulzky C, Hoffmann K H, Random walks on finitely ramified Sierpinski carpets, CPC 134, 307 (2001)

Davison M, Essex C, Schulzky C, Franz A, Hoffmann K H, Clouds, fibres and echoes: a new approach to studying random walks on fractals, JPA 34, L289 (2001)

Kunz M, Random walks and localization on the Penrose lattice, PB 293, 164 (2000)

Jafarizadeh M A, Mirzaee M, Aghlara H, Hierarchy of critical exponents on Sierpinsky fractal resistor networks, cond-mat/0005338

de Almeida R M C, Lemke N, Campbell I A, Stretched Exponential Relaxation on the Hypercube and the Glass Transition, cond-mat/0003351

Kozak J J, Random walks on a fractal solid, JSP 101, 405 (2000)

Acedo L, Yuste S B, Short-time regime propagator in fractals, PRE 57, 5160 (1998)

Porra J M, Yuste S B, Demonstration of a conjecture for random walks in d-dimensional Sierpinski fractals, JPA 31, 6589 (1998)

Aarao Reis F D A, Scaling for random walks on Sierpinski carpets, PLA 214, 239 (1996)

Aarao Reis F D A, Diffusion on regular random fractals, JPA 29, 7803 (1996)

Hattori T, Nakajima H, Transition density of diffusion on the Sierpinski gasket and extension of Flory's formula, PRE 52, 1202 (1995)

Klafter J, Zumofen G, Blumen A, On the propagator of Sierpinski gaskets, JPA 24, 4835 (1991)

Taitelbaum H, Danino M, Havlin S, Webman I, Transport in networks with a power-law distribution of conductances: The ladder and the Sierpinski gasket, PRB 41, 2445 (1990)

Bunde A, Havlin S, Roman H E, Multifractal features of random walks on random fractals, PRA 42, 6274 (1990)

Argyrakis P, Anacker L W, Kopelman R, Random walks on fractals: higher moments, JPA 21, 569 (1988)

Guyer R A, Diffusive motion on a fractal; Gnm(t), PRA 32, 2324 (1985)

Guyer R A, Random walking on a fractal, PRA 30, 1112 (1984)

Guyer R A, Diffusion on the Sierpinski gaskets: A random walker on a fractally structured object, PRA 29, 2751 (1984)

Hilfer R, Blumen A, Renormalization on Sierpinski-type fractals, JPA 17, L537 (1984)

Gould H, Kohin R P, Diffusion on lattice animals and percolation clusters: a renormalisation group approach, JPA 17, L159 (1984)

Gefen Y, Aharony A, Shapir Y, Mandelbrot B B, Phase transitions on fractals. II. Sierpinski gaskets, JPA 17, 435 (1984)

Gefen Y, Aharony A, Mandelbrot B B, Phase transitions on fractals. I. Quasi-linear lattices, JPA 16, 1267 (1983)

Given J A, Mandelbrot B B, Diffusion on fractal lattices and the fractal Einstein relation, JPB 16, L565 (1983)

d'Auriac A J C, Benoit A, Rammal R, Random walk on fractals: numerical studies in two dimensions, JPA 16, 4039 (1983)

Rammal R, Spectrum of harmonic excitations on fractals, J Physique 45, 191 (1984)

Gefen Y, Aharony A, Mandelbrot B B, Kirkpatrick S, Solvable fractal family and its possible relation to the backbone at percolation, PRL 47, 1771 (1981)

Random walk on trees

Movaghar B, Pohlmann B, Schirmacher W, Random walk in disordered hopping systems, Solid State Comm 34, 451 (1980)

Fisher M E, Essam J W, Some cluster size and percolation problems, JMP 2, 609 (1961)

Complex models

Hattori T, Tsuda T, Renormalization group analysis of the self-avoiding paths on the d-dimensional Sierpinski gaskets, JSP 109, 39 (2002)

Ordemann A, Porto M, Roman H E, Self-avoiding walks on Sierpinski lattices in two and three dimensions, PRE 65, 021107 (2002)

Ordemann A, Porto M, Roman H E, Self-avoiding walks on self-similar structures: finite versus infinite ramification, JPA 35, 8029 (2002)

Maricic J, Elezovic-Hadzic S, Interacting linear polymers on three-dimensional Sierpinski fractals, cond-mat/0205509

Broeck C Van den, Waiting times for random walks on regular and fractal lattices, PRL 62, 1421 (1989)

First passage time

Y Meroz, I Sokolov, J Klafter, Distribution of first-passage times to specific targets on compactly explored fractal structures, PRE 83, 020104 (2011) – doi

Chelminiak P, Kurzynski M, Mean first-passage time for diffusion on fractal lattices with imposed boundary conditions, PA 342, 507 (2004)

Kozak J J, Balakrishnan V, Analytic expression for the mean time to absorption for a random walker on the Sierpinski gasket, PRE 65, 021105 (2002)

Van den Broeck C, Renormalization of first-passage times for random walks on deterministic fractals, PRA 40, 7334 (1989)

Trapping

Blumen A, Klafter J, Zumofen G, Trapping and reaction rates on fractals: A random-walk study, PRB 28, 6112 (1983)

Miscellaneous

Stajic J, Elezovic-Hadzic S, Hamiltonian walks on Sierpinski and n-simplex fractals, JPA 38, 5677 (2005)

Schulz B M, Schulz M, Trimper S, Random walks with feedback on fractal lattices, PRE 66, 031106 (2002)

Milosevic S, Zivic I, Elezovic-Hadzic S, Comment on ''Critical behavior of the chain-generating function of self-avoiding walks on the Sierpinski gasket family: The Euclidean limit'', PRE 61, 2141 (2000)

Pitsianis N, Bleris G L, Argyrakis P, Information dimension in fractal structures, PRB 39, 7097 (1989)

O'Shaughnessy B, Procaccia I, Diffusion on fractals, PRA 32, 3073 (1985)

Dasgupta R, Ballabh T K, Tarafdar S, Scaling exponents for random walks on Sierpinski carpets and number of distinct sites visited: a new algorithm for infinite fractal lattices, JPA 32, 6503 (1999) – cor

Matan O, Havlin S, Stauffer D, Scaling properties of diffusion on comb-like structures, JPA 22, 2867 (1989)

Incorrect papers