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Recursions and tightness for the maximum of the discrete, two dimensional Gaussian free field


Bolthausen, E; Deuschel, J D; Zeitouni, Ofer (2011). Recursions and tightness for the maximum of the discrete, two dimensional Gaussian free field. Electronic Communications in Probability, 16:114-119.

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 F. M. Dekking and B. Host [Probab. Theory Relat. Fields 90, No. 3, 403–426 (1991; Zbl 0734.60074)] for branching random walks with bounded increments and on comparison results specific to Gaussian fields.

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 F. M. Dekking and B. Host [Probab. Theory Relat. Fields 90, No. 3, 403–426 (1991; Zbl 0734.60074)] for branching random walks with bounded increments and on comparison results specific to Gaussian fields.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Language:English
Date:16 February 2011
Deposited On:14 Mar 2013 07:34
Last Modified:24 Apr 2024 03:37
Publisher:Institute of Mathematical Statistics
ISSN:1083-589X
OA Status:Gold
Publisher DOI:https://doi.org/10.1214/ECP.v16-1610
  • Content: Published Version
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)