Extremal process of the zero-average Gaussian free field for d≥3
Statistics and Probability Letters
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≥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.
Das, Sayan and Hazra, Rajat Subhra, "Extremal process of the zero-average Gaussian free field for d≥3" (2019). Journal Articles. 937.