Random walks on Sierpinski gaskets of different dimensions

Sebastian Weber, Joseph Klafter, Alexander Blumen

Research output: Contribution to journalArticlepeer-review

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 ds 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 ds, a question of great practical relevance.

Original languageEnglish
Article number051129
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume82
Issue number5
DOIs
StatePublished - 23 Nov 2010

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