A note on the extremal process of the supercritical Gaussian Free Field

Alberto Chiarini; Alessandra Cipriani; Rajat Subhra Hazra

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arXiv · 1505.05324

A note on the extremal process of the supercritical Gaussian Free Field

Alberto Chiarini·Alessandra Cipriani·Rajat Subhra Hazra

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Abstract

We consider both the infinite-volume discrete Gaussian Free Field (DGFF) and the DGFF with zero boundary conditions outside a finite box in dimension larger or equal to 3. We show that the associated extremal process converges to a Poisson point process. The result follows from an application of the Stein-Chen method from Arratia et al. (1989).

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Alberto Chiarini, Alessandra Cipriani, Rajat Subhra Hazra. 2015-05-20. A note on the extremal process of the supercritical Gaussian Free Field. https://arxiv.org/abs/1505.05324

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