Memory-induced anomalous dynamics: emergence of diffusion, subdiffusion, and superdiffusion from a single random walk model

TL;DR

This paper introduces a non-Markovian, analytically tractable random walk model that can exhibit subdiffusion, diffusion, and superdiffusion by adjusting parameters, providing insights into diverse anomalous diffusion behaviors.

Contribution

The paper presents a single, parameter-dependent random walk model capable of generating all three types of anomalous diffusion behaviors, a novel unification in the field.

Findings

Model exhibits subdiffusive, diffusive, and superdiffusive regimes.

Analytic tractability of the model allows detailed analysis.

Provides insights into mechanisms behind different anomalous diffusion types.

Abstract

We present a random walk model that exhibits asymptotic subdiffusive, diffusive, and superdiffusive behavior in different parameter regimes. This appears to be the first instance of a single random walk model leading to all three forms of behavior by simply changing parameter values. Furthermore, the model offers the great advantage of analytic tractability. Our model is non-Markovian in that the next jump of the walker is (probabilistically) determined by the history of past jumps. It also has elements of intermittency in that one possibility at each step is that the walker does not move at all. This rich encompassing scenario arising from a single model provides useful insights into the source of different types of asymptotic behavior.