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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.
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.
| 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 Oct 2024 03:32 |
| Publisher: | Institute of Mathematical Statistics |
| ISSN: | 1083-589X |
| OA Status: | Gold |
| Publisher DOI: | https://doi.org/10.1214/ECP.v16-1610 |
Bolthausen, E