Transport aspects in anomalous diffusion: Lévy walks

A. Blumen*, G. Zumofen, J. Klafter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper we present a combined analytical and numerical study of transport properties of Lévy walks. Here, within the framework of continuous-time random walks (CTRW) with coupled memories, we focus on the probability P0(t) of being at the initial site at time t and on S(t), the mean number of distinct sites visited in time t. We use the connection between P0(t) and S(t), which are related via their Laplace transform, and we reanalyze our previous findings for r2(t), the mean-squared displacement. Furthermore, S(t) shows, as a function of the memory parameters, a very interesting, nonuniversal, nonmonotonic behavior, which we corroborate by numerical simulations in one dimension. We compare the findings with those for decoupled CTRWs on regular lattices and on fractals.

Original languageEnglish
Pages (from-to)3964-3973
Number of pages10
JournalPhysical Review A
Issue number7
StatePublished - 1989


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