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

Understand

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).