WIAS Preprint No. 2111, (2015)

A note on the extremal process of the supercritical Gaussian free field



Authors

  • Chiarini, Alberto
  • Cipriani, Alessandra
  • Hazra, Rajat Subhra

2010 Mathematics Subject Classification

  • 60G15 60G30 60G55 60G70 82B41

Keywords

  • Gaussian free field, Poisson approximation, point processes, extremal process, Stein--Chen method

Abstract

We consider both the infinite-volume discrete Gaussian Free Field (DGFF) and the DGFF with zero boundary conditions outside a finite boxin 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).

Appeared in

  • Electron. Comm. Probab., 20 (2015) pp. 74/1--74/10.

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