Work

Random walks on fractal structures and percolation clusters

Year: 1983

Type: article

Abstract: The notion of spectral dimensionality of a self-similar (fractal) structure is recalled, and its value for the family of Sierpinski gaskets derived via a scaling argument. Various random walk properties such as the probability of closed walks and the mean number of visited sites are shown to be governed by this spectral dimension. It is suggested that the number SN of distinct sites visited during an N-step random walk on an infinite cluster at percolation threshold varies asymptotically as : SN ∼ N2/3, in any dimension.

Source: Journal de Physique Lettres

DOI: 10.1051/jphyslet:0198300440101300

Authors: R. Rammal, G. Toulouse

Institution: Laboratoire de Physique de l'Ecole Normale Supérieure

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2138085462

FWCI: 90.62

Cites: 8

Cited by: 971

Related to: 10