The mean number of distinct sites visited by an elephant random walker in one-dimension

Abstract

Schütz and Trimper in 2004 introduced a non-Markovian random walk that involved a random walker that has access to the complete history of what it has done in the past and uses this knowledge to influence its future motion. Today, this random walk is known as the elephant random walk. In this work, we have analyzed the mean number of distinct sites visited by an elephant random walker in one-dimension, numerically. It was found that varying the value of the initial step parameter q did not affect the mean number of distinct sites visited by an elephant random walker. It was also found that high values of the memory parameter, p, causes the elephant random walker to visit more sites per time step specially in the superdiffusive case of the elephant random walk, i.e. p ≥ 3/4 , where the rate of increase in the mean number of distinct sites visited per time step is more drastic as opposed to the rates for the normal diffusive elephant random walkers.