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).
|Number of pages||14|
|Publication status||Published - 1 Jan 2016|
- Extreme value theory
- Gaussian free field
- Stein-Chen method