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

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  • Das, Sayan
  • Hazra, Rajat Subhra

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.

Suggested Citation

  • Das, Sayan & Hazra, Rajat Subhra, 2019. "Extremal process of the zero-average Gaussian free field for d≥3," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 42-49.
    • Handle: RePEc:eee:stapro:v:146:y:2019:i:c:p:42-49
    DOI: 10.1016/j.spl.2018.10.020
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