  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.
