The influence of statistical properties of Fourier coefficients on random surfaces

TL;DR

This paper investigates how the statistical properties of Fourier coefficients, including modulus and phase distributions, influence the characteristics of Gaussian random surfaces and their scale invariance.

Contribution

It demonstrates that the scale invariance of Gaussian surfaces is unaffected by the modulus distribution but is influenced by the phase distribution.

Findings

Scale invariance persists regardless of modulus distribution.

Non-uniform phase distributions alter surface properties.

Fourier phase distribution impacts surface morphology.

Abstract

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.