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We show experimentally and theoretically that the persistence of large deviations in equilibrium step fluctuations is characterized by an infinite family of independent exponents. These exponents are obtained by carefully analyzing dynamical experimental images of Al/Si(111) and Ag(111) equilibrium steps fluctuating at high (970K) and low (320K) temperatures respectively, and by quantitatively interpreting our observations on the basis of the corresponding coarse-grained discrete and continuum theoretical models for thermal surface step fluctuations under attachment/detachment (``high-temperature) and edge-diffusion limited kinetics (``low-temperature) respectively.
Numerical and analytic results for the exponent theta describing the decay of the first return probability of an interface to its initial height are obtained for a large class of linear Langevin equations. The models are parametrized by the dynamic r
Results of analytic and numerical investigations of first-passage properties of equilibrium fluctuations of monatomic steps on a vicinal surface are reviewed. Both temporal and spatial persistence and survival probabilities, as well as the probabilit
The effects of sampling rate and total measurement time have been determined for single-point measurements of step fluctuations within the context of first-passage properties. Time dependent STM has been used to evaluate step fluctuations on Ag(111)
We investigate solid-on-solid models that belong to the Kardar-Parisi-Zhang (KPZ) universality class on substrates that expand laterally at a constant rate by duplication of columns. Despite the null global curvature, we show that all investigated mo
We report on the residence times of capillary waves above a given height $h$ and on the typical waiting time in between such fluctuations. The measurements were made on phase separated colloid-polymer systems by laser scanning confocal microscopy. Du