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arXiv · 1304.5577

Distributional Ergodicity in Stored-Energy-Driven Lévy Flights

Takuma Akimoto·Tomoshige Miyaguchi
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Abstract

We study a class of random walk, the stored-energy-driven Lévy flight (SEDLF), whose jump length is determined by a stored energy during a trapped state. The SEDLF is a continuous-time random walk with jump lengths being coupled with the trapping times. It is analytically shown that the ensemble-averaged mean square displacements exhibit subdiffusion as well as superdiffusion, depending on the coupling parameter. We find that time-averaged mean square displacements increase linearly with time and the diffusion coefficients are intrinsically random, a manifestation of {\it distributional ergodicity}. The diffusion coefficient shows aging in subdiffusive regime, whereas it increases with the measurement time in superdiffusive regime.

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Takuma Akimoto, Tomoshige Miyaguchi. 2013-06-25. Distributional Ergodicity in Stored-Energy-Driven Lévy Flights. https://doi.org/10.1103/physreve.87.062134

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