2013/12/31 by A. Rebenshtok, S. Denisov, Peter Hänggi +3 · 5 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Anomalous diffusion #Central limit theorem #Complex Systems and Time Series Analysis #Covariant transformation #Diffusion #Fractal #Fractional Differential Equations Solutions #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Multifractal system #Nonlinear system #Physics #Quantum mechanics #Statistical physics #cond-mat.stat-mech #nlin.CD #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physrevlett.112.110601
published as Phys. Rev. Lett. 112, 110601 (2014) · PRL, in press
arxiv created 2014/02/07 · openalex publication_date 2014/03/17 · arxiv updated 2014/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.