Header

UZH-Logo

Maintenance Infos

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


Bolthausen, E; Deuschel, J D; Zeltoni, O (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.

Statistics

Citations

Dimensions.ai Metrics

18 citations in Scopus®
25 citations in Microsoft Academic
Google Scholar™

Altmetrics

Downloads

34 downloads since deposited on 14 Mar 2013
8 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:16 February 2011
Deposited On:14 Mar 2013 07:34
Last Modified:17 Feb 2018 15:52
Publisher:Institute of Mathematical Statistics
ISSN:1083-589X
OA Status:Green
Publisher DOI:https://doi.org/10.1214/ECP.v16-1610

Download

Download PDF  'Recursions and tightness for the maximum of the discrete, two dimensional Gaussian free field'.
Preview
Content: Published Version
Filetype: PDF
Size: 128kB
View at publisher