Anomalous diffusion originated by two Markovian hopping-trap mechanisms

TL;DR

This paper demonstrates through simulations that anomalous diffusion can arise from a random walk driven by two Markovian hopping-trap mechanisms, capturing key features observed in living systems.

Contribution

It introduces a model with two Markovian mechanisms that explains the core features of anomalous diffusion, including distribution transitions and Brownian yet non-Gaussian behavior.

Findings

Distribution transitions from exponential to Gaussian observed

Model reproduces Brownian yet non-Gaussian behavior

Matching features of anomalous diffusion in living systems

Abstract

We show through intensive simulations that the paradigmatic features of anomalous diffusion are indeed the features of a (continuous-time) random walk driven by two different Markovian hopping-trap mechanisms. If $p \in (0,1/2)$ and $1-p$ are the probabilities of occurrence of each Markovian mechanism, then the anomalousness parameter $\beta \in (0,1)$ results to be $\beta \simeq 1 - 1/\{1 + \log[(1-p)/p]\}$. Ensemble and single-particle observables of this model have been studied and they match the main characteristics of anomalous diffusion as they are typically measured in living systems. In particular, the celebrated transition of the walker's distribution from exponential to stretched-exponential and finally to Gaussian distribution is displayed by including also the Brownian yet non-Gaussian interval.