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The influence of statistical properties of Fourier coefficients on random Gaussian surfaces

2017; Nature Portfolio; Volume: 7; Issue: 1 Linguagem: Inglês

10.1038/s41598-017-02135-y

2045-2322

Caio P. de Castro, Mirko Luković, Roberto F. S. Andrade, Hartmut Herrmann,

Stochastic processes and statistical mechanics

Many examples of natural systems can be described by random Gaussian surfaces. Much can be learned by analyzing the Fourier expansion of the surfaces, from which it is possible to determine the corresponding Hurst exponent and consequently establish the presence of scale invariance. We show that this symmetry is not affected by the distribution of the modulus of the Fourier coefficients. Furthermore, we investigate the role of the Fourier phases of random surfaces. In particular, we show how the surface is affected by a non-uniform distribution of phases.