Extremes of some Gaussian random interfaces

TL;DR

This paper establishes a general criterion for certain dependent Gaussian models to belong to the Gumbel domain of attraction, demonstrating convergence of associated point processes and applying results to well-known Gaussian interface models.

Contribution

It provides a new criterion for Gaussian models to exhibit Gumbel extreme value behavior and proves convergence of related point processes, extending understanding of Gaussian interfaces.

Findings

Gaussian models satisfy the Gumbel domain of attraction

Convergence of the associated point process is proven

Conditions are verified for several Gaussian interface models

Abstract

In this article we give a general criterion for some dependent Gaussian models to belong to maximal domain of attraction of Gumbel, following an application of the Stein-Chen method studied in Arratia et al(1989). We also show the convergence of the associated point process. As an application, we show the conditions are satisfied by some of the well-known supercritical Gaussian interface models, namely, membrane model, massive and massless discrete Gaussian free field, fractional Gaussian free field.