We study simple diffusion where a particle stochastically resets to its initial position at a constant rate $r$. A finite resetting rate leads to a nonequilibrium stationary state with non-Gaussian fluctuations for the particle position. We also show that the mean time to find a stationary target by a diffusive searcher is finite and has a minimum value at an optimal resetting rate $r^{*}$. Resetting also alters fundamentally the late time decay of the survival probability of a stationary target when there are multiple searchers: while the typical survival probability decays exponentially with time, the average decays as a power law with an exponent depending continuously on the density of searchers.

• Received 14 February 2011

DOI:https://doi.org/10.1103/PhysRevLett.106.160601