  We report subnanometer, high-bandwidth measurements of the out-of-plane
(vertical) motion of atoms in freestanding graphene using scanning tunneling
microscopy. By tracking the vertical position over a long time period, a
1000-fold increase in the ability to measure space-time dynamics of atomically
thin membranes is achieved over the current state-of-the-art imaging
technologies. We observe that the vertical motion of a graphene membrane
exhibits rare long-scale excursions characterized by both anomalous
mean-squared displacements and Cauchy-Lorentz power law jump distributions.
