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

Alberto Chiarini; Alessandra Cipriani; Rajat Subhra Hazra

doi:10.1214/ECP.v20-4332

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

Alberto Chiarini, Alessandra Cipriani, Rajat Subhra Hazra

Research output: Contribution to journal › Article › Scientific › peer-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 language	English
Article number	74
Pages (from-to)	1-10
Number of pages	10
Journal	Electronic Communications in Probability
Volume	20
DOIs	https://doi.org/10.1214/ECP.v20-4332
Publication status	Published - 2015
Externally published	Yes

Keywords

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

Access to Document

10.1214/ECP.v20-4332

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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)",

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AU - Cipriani, Alessandra

AU - Hazra, Rajat Subhra

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N2 - 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)

AB - 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)

KW - Extremal process

KW - Gaussian free field

KW - Point processes

KW - Poisson approximation

KW - Stein–Chen method

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