Extremes of the supercritical Gaussian Free Field

Authors

Alberto Chiarini, Technische Universität Berlin
Alessandra Cipriani, Weierstrass Institute for Applied Analysis and Stochastics
Rajat Subhra Hazra, Indian Statistical Institute, Kolkata

Article Type

Research Article

Publication Title

Alea (Rio de Janeiro)

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).

First Page

711

Last Page

724

DOI

10.30757/alea.v13-28

Publication Date

1-1-2016

Comments

Open Access; Bronze Open Access; Green Open Access

Recommended Citation

Chiarini, Alberto; Cipriani, Alessandra; and Hazra, Rajat Subhra, "Extremes of the supercritical Gaussian Free Field" (2016). Journal Articles. 4207.
https://digitalcommons.isical.ac.in/journal-articles/4207