Non-normalizable densities in strong anomalous diffusion: Beyond the central limit theorem

Adi Rebenshtok, Sergey Denisov, Peter Hänggi, Eli Barkai

Research output: Contribution to journalArticlepeer-review


Strong anomalous diffusion, where 〈|x(t)|q〉∼tqν(q) with a nonlinear spectrum ν(q)≠const, is wide spread and has been found in various nonlinear dynamical systems and experiments on active transport in living cells. Using a stochastic approach we show how this phenomenon is related to infinite covariant densities; i.e., the asymptotic states of these systems are described by non-normalizable distribution functions. Our work shows that the concept of infinite covariant densities plays an important role in the statistical description of open systems exhibiting multifractal anomalous diffusion, as it is complementary to the central limit theorem.

Original languageEnglish
Article number110601
JournalPhysical Review Letters
Issue number11
StatePublished - 17 Mar 2014

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)


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