title: Diffusion with stochastic resetting at power-law times.
abstract: What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals τ distributed as a power law ∼τ^{-(1+α)};α>0? Modeling the stochastic process by diffusion and the large changes as abrupt resets to the initial condition, we obtain exact closed-form expressions for both static and dynamic quantities, while accounting for strong correlations implied by a power law. Our results show that the resulting dynamics exhibits a spectrum of rich long-time behavior, from an ever-spreading spatial distribution for α<1, to one that is time independent for α>1. The dynamics has strong consequences on the time to reach a distant target for the first time; we specifically show that there exists an optimal α that minimizes the mean time to reach the target, thereby offering a step towards a viable strategy to locate targets in a crowded environment.
authors.affiliation: Indian Institute of Space Science and Technology, Thiruvananthapuram, Kerala, India.
authors.forename: Apoorva
authors.initials: A
authors.lastname: Nagar
authors.affiliation: Max Planck Institute for the Physics of Complex Systems, Noethnitzer Straße 38, D-01187 Dresden, Germany.
authors.forename: Shamik
authors.initials: S
authors.lastname: Gupta