Stochastic dynamics of a non-Markovian random walk in the presence of resetting

Abstract

The discrete stochastic dynamics of a random walker in the presence of resetting and memory is analyzed. Resetting and memory effects may compete for certain parameter regime and lead to significant changes in the long time dynamics of the walker. Analytic exact results are obtained for a model memory where the walker remembers all the past events equally. In most cases, resetting effects dominate at long times and dictate the asymptotic dynamics. We discuss the full phase diagram of the asymptotic dynamics and the resulting changes due to the resetting and the memory effects.