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Extremal process of the zero-average Gaussian Free Field for $d\ge 3$
Sayan Das, Rajat Subhra Hazra · 2018-08-10 · via math.PR updates on arXiv.org

We consider the Gaussian free field on the torus whose covariance kernel is given by the zero-average Green's function. We show that for dimension $d\ge 3$, the extremal point process associated with this field converges weakly to a Poisson random measure. As an immediate corollary, the maxima of the field converges after appropriate centering and scaling to the Gumbel distribution.

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