Survival probability of random walks and Lévy flights with stochastic resetting

Abstract We perform a thorough analysis of the survival probability symmetric random walks with stochastic resetting, defined as for walker not to cross origin up time n . For continuous distributions step lengths either finite (random walks) or infinite variance (Lévy flights), this can be expressed in terms walk without given by Sparre Andersen theory. It is therefore universal, i.e. independent length distribution. analyze at depth, deriving both exact results times and asymptotic late-time results. also investigate case where distribution but continuous, focusing our attention onto arithmetic generating on lattice integers. detail example simple Polya propose an algebraic approach larger range.