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Miyaguchi T, Akimoto T. Ultraslow convergence to ergodicity in transient subdiffusion. Phys Rev E Stat Nonlin Soft Matter Phys. 2011;83(6):062101doi: 10.1103/PhysRevE.83.062101.
Miyaguchi, T., & Akimoto, T. (2011). Ultraslow convergence to ergodicity in transient subdiffusion. Physical review. E, Statistical, nonlinear, and soft matter physics, 83(6), 062101. https://doi.org/10.1103/PhysRevE.83.062101
Miyaguchi, Tomoshige, and Akimoto, Takuma. "Ultraslow convergence to ergodicity in transient subdiffusion." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 83,6 (2011): 062101. doi: https://doi.org/10.1103/PhysRevE.83.062101
Miyaguchi T, Akimoto T. Ultraslow convergence to ergodicity in transient subdiffusion. Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6):062101. doi: 10.1103/PhysRevE.83.062101. Epub 2011 Jun 15. PMID: 21797421.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6):062101. doi: 10.1103/PhysRevE.83.062101. Epub 2011 Jun 15.

Ultraslow convergence to ergodicity in transient subdiffusion.

Physical review. E, Statistical, nonlinear, and soft matter physics

Tomoshige Miyaguchi, Takuma Akimoto

Affiliations

  1. Department of Applied Physics, Osaka City University, Osaka, Japan. [email protected]

PMID: 21797421 DOI: 10.1103/PhysRevE.83.062101

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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