WIAS Preprint No. 2105, (2015)

Extremes of the supercritical Gaussian free field



Authors

  • Chiarini, Alberto
  • Cipriani, Alessandra
  • Hazra, Rajat Subhra

2010 Mathematics Subject Classification

  • 60K35 60G15 60G60 60G70

Keywords

  • discrete Gaussian free field, extreme value theory, Gumbel distribution, Stein-Chen method

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).

Appeared in

  • ALEA Lat. Am. J. Probab. Math. Stat., 13 (2016), pp. 711--724.

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