Electronic Communications in Probability

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

Alberto Chiarini, Alessandra Cipriani, and Rajat Hazra

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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).

Article information

Source
Electron. Commun. Probab., Volume 20 (2015), paper no. 74, 10 pp.

Dates
Accepted: 15 October 2015
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465321001

Digital Object Identifier
doi:10.1214/ECP.v20-4332

Mathematical Reviews number (MathSciNet)
MR3417446

Zentralblatt MATH identifier
1329.60147

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60G30: Continuity and singularity of induced measures 60G55: Point processes 60G57: Random measures 60G70: Extreme value theory; extremal processes 82B41: Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]

Keywords
Discrete Gaussian Free Field Stein-Chen method extremal process Poisson process approximation

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Chiarini, Alberto; Cipriani, Alessandra; Hazra, Rajat. A note on the extremal process of the supercritical Gaussian Free Field. Electron. Commun. Probab. 20 (2015), paper no. 74, 10 pp. doi:10.1214/ECP.v20-4332. https://projecteuclid.org/euclid.ecp/1465321001


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