Abstract
Stochastic surface growth driven by surface tension (Edwards-Wilkinson model) is investigated. The much studied stationary state, characterized by Gaussian distributed Fourier modes with power-law dispersion, is reexamined here to include extremal value statistics. We calculate the probability distribution of the largest Fourier intensity and find that, generically, it does not obey any of the known extreme statistics limit distributions, apart from special border cases where the Fisher-Tippett-Gumbel (FTG) distribution emerges. If a gap is, however, introduced in the dispersion then necessarily the FTG distribution is recovered.
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