Statistics of extremal intensities for Gaussian interfaces

TL;DR

This paper investigates the statistical behavior of extremal Fourier intensities in Gaussian interfaces, revealing that their distribution generally differs from known extreme value laws but converges to Gumbel in specific scenarios.

Contribution

It provides the first detailed analysis of extremal Fourier intensities for Gaussian interfaces with power-law dispersion, identifying conditions for Gumbel distribution emergence.

Findings

Maximal intensity distribution differs from integrated power spectrum.

Gumbel distribution appears in white noise, high dimensions, and short-wavelength modes.

Novel scenarios for Gumbel limit distribution emergence.

Abstract

The extremal Fourier intensities are studied for stationary Edwards-Wilkinson-type, Gaussian, interfaces with power-law dispersion. We calculate the probability distribution of the maximal intensity and find that, generically, it does not coincide with the distribution of the integrated power spectrum (i.e. roughness of the surface), nor does it obey any of the known extreme statistics limit distributions. The Fisher-Tippett-Gumbel limit distribution is, however, recovered in three cases: (i) in the non-dispersive (white noise) limit, (ii) for high dimensions, and (iii) when only short-wavelength modes are kept. In the last two cases the limit distribution emerges in novel scenarios.