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Extremes of the supercritical Gaussian Free Field

Published 29 Apr 2015 in math.PR | (1504.07819v4)

Abstract: We show that the rescaled maximum of the discrete Gaussian Free Field (DGFF) in dimension larger or equal to 3 is in the maximal domain of attraction of the Gumbel distribution. The result holds both for the infinite-volume field as well as the field with zero boundary conditions. We show that these results follow from an interesting application of the Stein-Chen method from Arratia et al. (1989).

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