Extremal process of the zero-average Gaussian free field for d≥3

Sayan Das and Rajat Subhra Hazra

Statistics & Probability Letters, 2019, vol. 146, issue C, 42-49

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≥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.

Keywords: Gaussian free field on torus; Zero-average Green’s function; Random interface; Extremes (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2018.10.020

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