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).
Highlights
In this article we study the behavior of the extremal process of the discrete Gaussian Free Field (DGFF) in dimension larger or equal to 3
We show that the associated extremal process converges to a Poisson point process
In this article we study the behavior of the extremal process of the DGFF in dimension larger or equal to 3
Summary
In this article we study the behavior of the extremal process of the DGFF in dimension larger or equal to 3 This extends the result presented in [9] in which the convergence of the rescaled maximum of the infinite-volume DGFF and the 0-boundary condition field was shown. The extremes of the DGFF in dimension 2 have deep connections with those of Branching Brownian Motion ([1, 2, 3, 4]) These works showed that the limiting point process is a randomly shifted decorated Poisson point process, and we refer to [15] for structural details.
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