瞬态亚扩散中的超慢收敛到遍历性
Ultraslow Convergence to Ergodicity in Transient Subdiffusion
摘要：
研究了具有截断$α$稳定捕获时间的连续时间随机游动.我们证明了分布遍历一类观测量，即，时间平均观测遵循概率密度函数称为Mittag-Leffler分布。这种分布遍历行为持续了很长时间，因此收敛到普通遍历性比捕获时间分布由普通分布给出的情况要慢得多。我们还发现了从分布遍历行为到普通遍历行为的交叉。
英文摘要：
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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