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October 2001 Entropic Repulsion and the Maximum of the two-dimensional harmonic
Erwin Bolthausen, Jean-Dominique Deuschel, Giambattista Giacomin
Ann. Probab. 29(4): 1670-1692 (October 2001). DOI: 10.1214/aop/1015345767


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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Erwin Bolthausen. Jean-Dominique Deuschel. Giambattista Giacomin. "Entropic Repulsion and the Maximum of the two-dimensional harmonic." Ann. Probab. 29 (4) 1670 - 1692, October 2001.


Published: October 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1034.82018
MathSciNet: MR1880237
Digital Object Identifier: 10.1214/aop/1015345767

Primary: 60G15 , 60K35 , 82B41

Keywords: effective interface models , Entropic repulsion , extrema of Gaussian fields , Free field , large deviations , multiscale decomposition

Rights: Copyright © 2001 Institute of Mathematical Statistics

Vol.29 • No. 4 • October 2001
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