Extremes of the supercritical Gaussian Free Field
Probability
2016-04-05 v4
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).
Keywords
Cite
@article{arxiv.1504.07819,
title = {Extremes of the supercritical Gaussian Free Field},
author = {Alberto Chiarini and Alessandra Cipriani and Rajat Subhra Hazra},
journal= {arXiv preprint arXiv:1504.07819},
year = {2016}
}
Comments
15 pages, 2 figures. Minor typos corrected, changed the proof of Theorem 2 (upper bound)