title: Random walks on Sierpinski gaskets of different dimensions.
abstract: We study random walks (RWs) on classical and dual Sierpinski gaskets (SG and DSG), naturally embedded in d-dimensional Euclidian spaces (ESs). For large d the spectral dimension d(s) approaches 2, the marginal RW dimension. In contrast to RW over two-dimensional ES, RWs over SG and DSG show a very rich behavior. First, the time discrete scale invariance leads to logarithmic-periodic (log-periodic) oscillations in the RW properties monitored, which increase in amplitude with d. Second, the asymptotic approach to the theoretically predicted RW power laws is significantly altered depending on d and on the variant of the fractal (SG or DSG) under study. In addition, we discuss the suitability of standard RW properties to determine d(s), a question of great practical relevance.
authors.affiliation: Freiburg Institute for Advanced Studies, University of Freiburg, Albertstr. 19, D-79104 Freiburg, Germany.
authors.forename: Sebastian
authors.initials: S
authors.lastname: Weber
authors.forename: Joseph
authors.initials: J
authors.lastname: Klafter
authors.forename: Alexander
authors.initials: A
authors.lastname: Blumen