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Entropic repulsion and the maximum of the two-dimensional harmonic crystal


Bolthausen, E; Deuschel, J-D; Giacomin, G (2001). Entropic repulsion and the maximum of the two-dimensional harmonic crystal. The Annals of Probability, 29(4):1670-1692.

Abstract

We consider the lattice version of the free field in two dimensions (also called harmonic crystal). The main aim of the paper is to discuss quantitatively the entropic repulsion of the random surface in the presence of a hard wall. The basic ingredient of the proof is the analysis of the maximum of the field which requires a multiscale analysis reducing the problem essentially to a problem on a field with a tree structure.

Abstract

We consider the lattice version of the free field in two dimensions (also called harmonic crystal). The main aim of the paper is to discuss quantitatively the entropic repulsion of the random surface in the presence of a hard wall. The basic ingredient of the proof is the analysis of the maximum of the field which requires a multiscale analysis reducing the problem essentially to a problem on a field with a tree structure.

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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
Uncontrolled Keywords:Free field, effective interface models, entropic repulsion, large deviations, extrema of Gaussian fields, multiscale decomposition
Language:English
Date:2001
Deposited On:27 Apr 2010 11:31
Last Modified:26 Jun 2022 22:35
Publisher:Institute of Mathematical Statistics
ISSN:0091-1798
Additional Information:© Institute of Mathematical Statistics
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1214/aop/1015345767