Anomalous diffusion originated by two Markovian hopping-trap mechanisms

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 is an element of (0, 1/2) and 1 - p are the probabilities of occurrence of each Markovian mechanism, then the anomalousness parameter beta is an element of (0, 1) results to be beta similar or equal to 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.

Automated summary

Through intensive simulations, it has been shown that the characteristic features of anomalous diffusion can be explained by a random walk driven by two different Markovian hopping-trap mechanisms. By studying ensemble and single-particle observables, it is found that this model matches the main characteristics of anomalous diffusion commonly observed in living systems. The transition of the walker's distribution from exponential to stretched-exponential and finally to Gaussian distribution can be observed by considering the inclusion of non-Gaussian intervals.