A note on the extremal process of the supercritical Gaussian Free Field

Alberto Chiarini, Alessandra Cipriani, Rajat Subhra Hazra

Research output: Contribution to journalArticleScientificpeer-review

12 Citations (Scopus)

Abstract

We consider both the infinite-volume discrete Gaussian Free Field (DGFF) and the DGFF with zero boundary conditions outside a finite box in dimension larger or equal to 3. We show that the associated extremal process converges to a Poisson point process. The result follows from an application of the Stein-Chen method from Arratia et al. (1989)

Original languageEnglish
Article number74
Pages (from-to)1-10
Number of pages10
JournalElectronic Communications in Probability
Volume20
DOIs
Publication statusPublished - 2015
Externally publishedYes

Keywords

  • Extremal process
  • Gaussian free field
  • Point processes
  • Poisson approximation
  • Stein–Chen method

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