A Test for Determining a Subdiffusive Model in Ergodic Systems from Single Trajectories

TL;DR

This paper introduces a statistical test to differentiate between types of subdiffusive behavior in ergodic systems based on single particle trajectories, aiding in identifying underlying physical mechanisms.

Contribution

It proposes a novel space-filling based statistical test to distinguish between trapping-induced and viscoelastic subdiffusion models, validated with synthetic data.

Findings

Test effectively differentiates trapping from viscoelastic subdiffusion.

Flow-chart guides decision-making for various subdiffusive models.

Validated with synthetic trajectories to demonstrate specificity.

Abstract

Experiments on particles' motion in living cells show that it is often subdiffusive. This subdiffusion may be due to trapping, percolation-like structures, or viscoelatic 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 non-ergodicity, 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.