Extreme values for two-dimensional discrete Gaussian free field

@article{Ding2012ExtremeVF,
  title={Extreme values for two-dimensional discrete Gaussian free field},
  author={Jian Ding and Ofer Zeitouni},
  journal={arXiv: Probability},
  year={2012}
}
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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