“…Detailed analyses for Brownian and fractional Brownian motion demonstrate that the power-law decay S k ( f , T ) ∼ 1/ f β is preserved in individual PSDs. In addition, similarly to the amplitude variations of the TA-MSD from one finite-time trajectory to the next, the PDF P k ( A ) of fluctuations of the PSD's amplitude A for different trajectories from the same ensemble show a characteristic behaviour, which has also been verified with experimental data, 154,210–212 as shown in the inset of Fig. 5c.…”