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.
The emergence of non-gaussian distributions for macroscopic quantities in nonequilibrium steady states is discussed with emphasis on the effective criticality and on the ensuing universality of distribution functions. The following problems are treated in more detail: nonequilibrium interface fluctuations (the problem of upper critical dimension of the Kardar-Parisi-Zhang equation), roughness of signals displaying Gaussian 1/f power spectra (the relationship to extreme-value statistics), effects of boundary conditions (randomness of the digits of π).
Conference Committee Involvement (2)
Fluctuations and Noise in Materials
26 May 2004 | Maspalomas, Gran Canaria Island, Spain
Second International Symposium on Fluctuations and Noise