  Significant and persistent trajectory-to-trajectory variance are commonly
observed in the particle tracking experiments, which have become a major
challenge for the experiment data analysis. In this theoretical paper, we
investigate the ergodicity recovery behavior, which helps to clarify the origin
and the convergence of trajectory-to-trajectory fluctuation in various
heterogeneous disordered media. The concepts of self-averaging and ergodicity
are revisited in the context of trajectory analysis. The slow ergodicity
recovery and the non-Gaussian diffusion in the annealed disordered media are
shown as the consequences of the central limit theorem in different situations.
The strange ergodicity recovery behavior is reported in the quenched disordered
case, which arises from a localization mechanism. The first-passage approach is
introduced to the ergodicity analysis for this case, of which the central limit
theorem can be employed and the ergodicity is recovered in the length scale of
diffusivity correlation.
