Anomalous diffusion in a symbolic model

TL;DR

This paper investigates the statistical properties of symbolic sequences generated by a power-law process, revealing diverse diffusive behaviors and aligning well with continuous-time random walk models, thus offering a simple framework for complex systems.

Contribution

It introduces a symbolic model with power-law symbol repetition to analyze anomalous diffusion, connecting it with continuous-time random walk theory.

Findings

Rich diffusive regimes including superdiffusion, subdiffusion, and normal diffusion.

Good agreement between numerical data and CTRW framework.

Model's potential applicability to real systems with power-law statistics.

Abstract

We address this work to investigate some statistical properties of symbolic sequences generated by a numerical procedure in which the symbols are repeated following a power law probability density. In this analysis, we consider that the sum of n symbols represents the position of a particle in erratic movement. This approach revealed a rich diffusive scenario characterized by non-Gaussian distributions and, depending on the power law exponent and also on the procedure used to build the walker, we may have superdiffusion, subdiffusion or usual diffusion. Additionally, we use the continuous-time random walk framework to compare with the numerical data, finding a good agreement. Because of its simplicity and flexibility, this model can be a candidate to describe real systems governed by power laws probabilities densities.