Elephant walk with single step memory lapse

Abstract

A discrete time random walk with full memory is called an Elephant walk. In this paper, we modify the Elephant walk by introducing a single step memory lapse. Recursion relations for the first two moments were obtained and were compared to the exact solutions of Schutz and Trimper for the nElephant walk. Plots suggest that the moments in the transient stages for the walkers with memory lapse behave differently as compared to that of the walker with full memory. This is caused by the Markovian nature of the second step for the walker with memory lapse. However, the long time behavior of the second moment of the walker with memory lapse follow a power law behavior similar to that of the Elephant walk solution.