Extremes of some Gaussian random interfaces

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.

arXiv commentTo appear in Journal of Statistical Physics

References in corpus (6)

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• Phase transition and level-set percolation for the Gaussian free field
• Convergence of the centered maximum of log-correlated Gaussian fields
• Extremes of the discrete two-dimensional Gaussian free field
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Cited by in corpus (5)

• Full extremal process, cluster law and freezing for the two-dimensional discrete Gaussian Free Field
• Extrema of the two-dimensional Discrete Gaussian Free Field
• Phase transition for level-set percolation of the membrane model in dimensions $d\ge 5$
• Pinning for the critical and supercritical membrane model
• Thermodynamic and Scaling Limits of the non-Gaussian Membrane Model