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We report the results of analytic and numerical investigations of the timescale of survival or non-zero-crossing probability $S(t)$ in equilibrium stepfluctuations described by Langevin equations appropriate forattachment/detachment and edge-diffusion limited kinetics. An exact relationbetween long-time behaviors of the survival probability and the autocorrelationfunction is established and numerically verified. $S(t)$ is shown to exhibitsimple scaling behavior as a function of system size and sampling time. Ourtheoretical results are in agreement with those obtained from an analysis ofexperimental dynamical STM data on step fluctuations on Al/Si(111) and Ag(111)surfaces.Comment: RevTeX, 4 pages, 3 figure

Survival in equilibrium step fluctuations