Extremes of the supercritical Gaussian free field
- Chiarini, Alberto
- Cipriani, Alessandra
- Hazra, Rajat Subhra
2010 Mathematics Subject Classification
- 60K35 60G15 60G60 60G70
- discrete Gaussian free field, extreme value theory, Gumbel distribution, Stein-Chen method
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).
- ALEA Lat. Am. J. Probab. Math. Stat., 13 (2016), pp. 711--724.