Stochastic pathway to anomalous diffusion

J. Klafter, A. Blumen, M. F. Shlesinger

Research output: Contribution to journalArticlepeer-review


We present an appraisal of differential-equation models for anomalous diffusion, in which the time evolution of the mean-square displacement is r2(t)∼tγ with γ1. By comparison, continuous-time random walks lead via generalized master equations to an integro-differential picture. Using Lévy walks and a kernel which couples time and space, we obtain a generalized picture for anomalous transport, which provides a unified framework both for dispersive (γ<1) and for enhanced diffusion (γ>1).

Original languageEnglish
Pages (from-to)3081-3085
Number of pages5
JournalPhysical Review A
Issue number7
StatePublished - 1987
Externally publishedYes


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