Extremal process of the zero-average Gaussian Free Field for $d\ge 3$

Sayan Das; Rajat Subhra Hazra

doi:10.1016/j.spl.2018.10.020

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arXiv · 1808.03500

Extremal process of the zero-average Gaussian Free Field for $d\ge 3$

Sayan Das·Rajat Subhra Hazra

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Abstract

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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Sayan Das, Rajat Subhra Hazra. 2018-08-10. Extremal process of the zero-average Gaussian Free Field for $d\ge 3$. https://doi.org/10.1016/j.spl.2018.10.020

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