Extrema of the planar Gaussian Free Field: convergence of the maximum using hidden tree structures

Extrema of the planar Gaussian Free Field: convergence of the maximum using hidden tree structures

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Ofer Zeitouni , New York University and Weizmann Institute
Fine Hall 322

In a recent work, Bramson, Ding and the speaker proved that the maximum of the Gaussian free field in a discrete box of side $N$, centered around its mean, converges in distribution to a shifted Gumbel. The proof uses branching random walks, modified branching random walks, and a modification of the classical second moment method. Underlying the proof is a hidden rough tree structure. I will explain the terms in the abstract, the structure of the proof, and will sketch applications to other related problems.