Anomalous processes with general waiting times: functionals and multi-point structure

Abstract

Many transport processes in nature exhibit anomalous diffusive properties with non-trivial scaling of the mean square displacement, e.g., diffusion of cells or of biomolecules inside the cell nucleus, where typically a crossover between different scaling regimes appears over time. Here, we investigate a class of anomalous diffusion processes that is able to capture such complex dynamics by virtue of a general waiting time distribution. We obtain a complete characterization of such generalized anomalous processes, including their functionals and multi-point structure, using a representation in terms of a normal diffusive process plus a stochastic time change. In particular, we derive analytical closed form expressions for the two-point correlation functions, which can be readily compared with experimental data.

Accepted in Phys. Rev. Lett

References in corpus (6)

• Anomalous transport in the crowded world of biological cells
• Lévy walks
• Anomalous dynamics of cell migration
• Anomalous Diffusion of Inertial, Weakly Damped Particles
• On distributions of functionals of anomalous diffusion paths
• Continuous Time Random Walks (CTRWs): Simulation of continuous trajectories

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