Convergence in law of the maximum of the two-dimensional discrete Gaussian free field

Authors:
  • MBMaury Bramson
    Maury Bramson
  • JDJian Ding
    Jian Ding
  • OZOfer Zeitouni
    Ofer Zeitouni
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Abstract
We consider the two-dimensional Gaussian Free Field on a box of side length $N$, with Dirichlet boundary data, and prove the convergence of the law of the recentered maximum of the field.