Maximum and entropic repulsion for a Gaussian membrane model in the critical dimension

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.

Published in at http://dx.doi.org/10.1214/08-AOP417 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Extremes of the discrete two-dimensional Gaussian free field
• Scaling limits of $(1+1)$-dimensional pinning models with Laplacian interaction
• Critical behavior of interacting surfaces with tension

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• Scaling limit of semiflexible polymers: a phase transition
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• Thermodynamic and Scaling Limits of the non-Gaussian Membrane Model