## Electronic Communications in Probability

### Recursions and tightness for the maximum of the discrete, two dimensional Gaussian Free Field

#### Abstract

We consider the maximum of the discrete two dimensional Gaussian free field in a box, and prove the existence of a (dense) deterministic subsequence along which the maximum, centered at its mean, is tight. The method of proof relies on an argument developed by Dekking and Host for branching random walks with bounded increments and on comparison results specific to Gaussian fields.

#### Article information

Source
Electron. Commun. Probab., Volume 16 (2011), paper no. 11, 114-119.

Dates
Accepted: 16 February 2011
First available in Project Euclid: 7 June 2016

https://projecteuclid.org/euclid.ecp/1465261967

Digital Object Identifier
doi:10.1214/ECP.v16-1610

Mathematical Reviews number (MathSciNet)
MR2772390

Zentralblatt MATH identifier
1236.60039

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60G60: Random fields

Keywords
Gaussian free field. Recursions

Rights

#### Citation

Bolthausen, Erwin; Deuschel, Jean-Dominique; Zeitouni, Ofer. Recursions and tightness for the maximum of the discrete, two dimensional Gaussian Free Field. Electron. Commun. Probab. 16 (2011), paper no. 11, 114--119. doi:10.1214/ECP.v16-1610. https://projecteuclid.org/euclid.ecp/1465261967

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