Statistics of extremal intensities for Gaussian interfaces

Area of Science:

• Statistical physics
• Surface growth phenomena
• Complex systems

Background:

• Stationary Edwards-Wilkinson-type interfaces are fundamental models in surface growth.
• Understanding the statistical properties of these interfaces, particularly extreme events, is crucial.

Purpose of the Study:

• To investigate the extremal Fourier intensities of stationary Edwards-Wilkinson-type, Gaussian interfaces with power-law dispersion.
• To calculate the probability distribution of the maximal intensity and compare it with other statistical measures.

Main Methods:

• Analysis of extremal Fourier intensities for Gaussian interfaces.
• Calculation of the probability distribution of the maximal intensity.
• Comparison with integrated power spectrum (roughness) and known extreme value statistics.

Main Results:

• The maximal intensity distribution generally differs from surface roughness and standard extreme value distributions.
• The Fisher-Tippett-Gumbel limit distribution is recovered in three specific cases: nondispersive (white noise) limit, high dimensions, and short-wavelength mode dominance.
• Nonconventional scenarios were observed for the emergence of the limit distribution in high dimensions and short-wavelength cases.

Conclusions:

• The extremal properties of these interfaces exhibit complex behavior not captured by simple statistical measures.
• The Fisher-Tippett-Gumbel distribution provides a relevant framework for understanding extreme intensities under specific limiting conditions.
• Further research into nonconventional extreme value statistics in complex systems is warranted.