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

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.

48 pages, 2 figures. Added in v3 Theorem 2.5 (alternative description of limit law), various minor corrections, and many explanations and additional details. Filled in v4 a gap in the proof of Lemma 3.10. Added more details in V5 and streamlined the argument in Section 5

References in corpus (1)

• Extreme local extrema of two-dimensional discrete Gaussian free field

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