Extremes of the supercritical Gaussian Free Field

Alberto Chiarini, Alessandra Cipriani, Rajat Subhra Hazra

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6 Citations (Scopus)

Abstract

We show that the rescaled maximum of the discrete Gaussian Free Field (DGFF) in dimension larger or equal to 3 is in the maximal domain of attraction of the Gumbel distribution. The result holds both for the infinite-volume field as well as the field with zero boundary conditions. We show that these results follow from an interesting application of the Stein-Chen method from Arratia et al. (1989).

Original languageEnglish
Pages (from-to)711-724
Number of pages14
JournalAlea
Volume13
Issue number2
Publication statusPublished - 2016

Keywords

  • Extreme value theory
  • Gaussian free field
  • Stein-Chen method

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  • Cite this

    Chiarini, A., Cipriani, A., & Hazra, R. S. (2016). Extremes of the supercritical Gaussian Free Field. Alea, 13(2), 711-724.