The impact of random memory resetting on a non-Markovian random walk

In this study, we present a discrete-time non-Markov process, referred to as an Elephant Random Walk, implemented on an infinite one-dimensional lattice, with the inclusion of random memory resetting. Upon each random resetting event, the walker completely loses its memory. Through analytical calculations, we determine the moments of displacement in the presence of random resetting. Our findings demonstrate that the process does not attain a steady state. However, the long-time behavior of the moments reveals that, under specific conditions, the displacement distribution follows a Gaussian distribution. By manipulating the resetting mechanism, the transition from diffusive to superdiffusive behavior, or vice versa, can be induced in the process.