Extreme values for two-dimensional discrete Gaussian free field

Jian Ding; Ofer Zeitouni

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arXiv · 1206.0346

Extreme values for two-dimensional discrete Gaussian free field

Jian Ding·Ofer Zeitouni

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Abstract

We consider in this paper the collection of near maxima of the discrete, two dimensional Gaussian free field in a box with Dirichlet boundary conditions. We provide a rough description of the geometry of the set of near maxima, estimates on the gap between the two largest maxima, and an estimate for the right tail up to a multiplicative constant on the law of the centered maximum.

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Jian Ding, Ofer Zeitouni. 2013-04-07. Extreme values for two-dimensional discrete Gaussian free field. https://arxiv.org/abs/1206.0346

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