Effects of scale-free avalanche walks on anomalous diffusions

Abstract

Effects of scale-free avalanche walks on anomalous diffusions have been studied by introducing simple non-Markovian walk models. The scale-free avalanche walk is realized as a walker goes to one direction consistently in a time interval, the distribution of which follows a power-law. And it is applied to the memory models, in which the entire history of a walk process is memorized or the memory for the latest step is enhanced with time. The power-law avalanche walk with memory effects strengthens the persistence between steps and thus makes the Hurst exponent be larger than the cases without avalanche walks, while does not affect the anti-persistent nature.