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March 2009 Maximum and entropic repulsion for a Gaussian membrane model in the critical dimension
Noemi Kurt
Ann. Probab. 37(2): 687-725 (March 2009). DOI: 10.1214/08-AOP417

Abstract

We consider the real-valued centered Gaussian field on the four-dimensional integer lattice, whose covariance matrix is given by the Green’s function of the discrete Bilaplacian. This is interpreted as a model for a semiflexible membrane. d=4 is the critical dimension for this model. We discuss the effect of a hard wall on the membrane, via a multiscale analysis of the maximum of the field. We use analytic and probabilistic tools to describe the correlation structure of the field.

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Noemi Kurt. "Maximum and entropic repulsion for a Gaussian membrane model in the critical dimension." Ann. Probab. 37 (2) 687 - 725, March 2009. https://doi.org/10.1214/08-AOP417

Information

Published: March 2009
First available in Project Euclid: 30 April 2009

zbMATH: 1166.60060
MathSciNet: MR2510021
Digital Object Identifier: 10.1214/08-AOP417

Subjects:
Primary: 31B30, 60K35, 82B41

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 2 • March 2009
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