The Annals of Probability

Entropic Repulsion and the Maximum of the two-dimensional harmonic

Erwin Bolthausen, Jean-Dominique Deuschel, and Giambattista Giacomin

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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.

Article information

Source
Ann. Probab., Volume 29, Number 4 (2001), 1670-1692.

Dates
First available in Project Euclid: 5 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1015345767

Digital Object Identifier
doi:10.1214/aop/1015345767

Mathematical Reviews number (MathSciNet)
MR1880237

Zentralblatt MATH identifier
1034.82018

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60G15: Gaussian processes 82B41: Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]

Keywords
Free field effective interface models entropic repulsion large deviations extrema of Gaussian fields multiscale decomposition

Citation

Bolthausen, Erwin; Deuschel, Jean-Dominique; Giacomin, Giambattista. Entropic Repulsion and the Maximum of the two-dimensional harmonic. Ann. Probab. 29 (2001), no. 4, 1670--1692. doi:10.1214/aop/1015345767. https://projecteuclid.org/euclid.aop/1015345767


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