Random walks on fractal structures and percolation clusters

R. Rammal , G. Toulouse

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.

Mots clés: percolation; random processes; fractal structures; percolation clusters; spectral dimensionality; Sierpinski gaskets; scaling argument; random walk; closed walks; infinite cluster; percolation threshold

Domaines: Articles anciens

R. Rammal, G. Toulouse. Random walks on fractal structures and percolation clusters. Journal de Physique Lettres, 1983, 44 (1), pp.13-22. ⟨10.1051/jphyslet:0198300440101300⟩. ⟨jpa-00232136⟩