Test for determining a subdiffusive model in ergodic systems from single trajectories

Experiments on particle motion show that it is often subdiffusive. This subdiffusion may be due to trapping, percolationlike structures, or viscoelastic behavior of the medium. While the models based on trapping (leading to continuous-time random walks) can easily be distinguished from the rest by testing their nonergodicity, the latter two cases are harder to distinguish. We propose a statistical test for distinguishing between these two based on the space-filling properties of trajectories, and prove its feasibility and specificity using synthetic data. We moreover present a flow chart for making a decision on a type of subdiffusion for a broader class of models.