Anomalous diffusion in a symbolic model

Anomalous diffusion in a symbolic model

H.V. Ribeiro, E.K. Lenzi, R.S. Mendes, and P.A. Santoro, Physica Scripta 83, 045007 (2011) PDF | DOI

In this work, we investigate some statistical properties of symbolic sequences generated by a numerical procedure in which the symbols are repeated following the 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 reveals a rich diffusive scenario characterized by non-Gaussian distribution and, depending on the power-law exponent or 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 the analytic results with the numerical data, thereby finding good agreement. Because of its simplicity and flexibility, this model can be a candidate for describing real systems governed by power-law probability
densities.