Ultraslow Convergence to Ergodicity in Transient Subdiffusion

Details Ultraslow Convergence to Ergodicity in Transient Subdiffusion Ultraslow Convergence to Ergodicity in Transient Subdiffusion

2011-02-04

arxiv.org/abs/1102.0829v2

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures

Scientific paper

We investigate continuous time random walks with truncated $\alpha$-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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