Fluctuating Interfaces Subject to Stochastic Resetting

We study one-dimensional fluctuating interfaces of length L, where the interface stochastically resets to a fixed initial profile at a constant rate r. For finite r in the limit L -> infinity , the system settles into a nonequilibrium stationary state with non-Gaussian interface fluctuations, which we characterize analytically for the Kardar-Parisi-Zhang and Edwards-Wilkinson universality class. Our results are corroborated by numerical simulations. We also discuss the generality of our results for a fluctuating interface in a generic universality class.