Ultraslow Convergence to Ergodicity in Transient Subdiffusion

Tomoshige Miyaguchi; Takuma Akimoto

doi:10.1103/physreve.83.062101

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arXiv · 1102.0829

Ultraslow Convergence to Ergodicity in Transient Subdiffusion

Tomoshige Miyaguchi·Takuma Akimoto

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Abstract

We investigate continuous time random walks with truncated $α$-stable trapping times. We prove distributional ergodicity for a class of observables; namely, the time-averaged observables follow the probability density function called the Mittag--Leffler distribution. This distributional ergodic behavior persists for a long time, and thus the convergence to the ordinary ergodicity is considerably slower than in the case in which the trapping-time distribution is given by common distributions. We also find a crossover from the distributional ergodic behavior to the ordinary ergodic behavior.

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BibTeX RIS

Tomoshige Miyaguchi, Takuma Akimoto. 2011-06-13. Ultraslow Convergence to Ergodicity in Transient Subdiffusion. https://doi.org/10.1103/physreve.83.062101

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