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Journal Article

Slow Levy flights

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Boyer,  Denis
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Citation

Boyer, D., & Pineda, I. (2016). Slow Levy flights. Physical Review E, 93(2), 2103-2103.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-B68F-8
Abstract
Among Markovian processes, the hallmark of Levy flights is superdiffusion, or faster-than-Brownian dynamics. Here we show that Levy laws, as well as Gaussian distributions, can also be the limit distributions of processes with long-range memory that exhibit very slow diffusion, logarithmic in time. These processes are path dependent and anomalous motion emerges from frequent relocations to already visited sites. We show how the central limit theorem is modified in this context, keeping the usual distinction between analytic and nonanalytic characteristic functions. A fluctuation-dissipation relation is also derived. Our results may have important applications in the study of animal and human displacements.