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

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

2008-01-03

arxiv.org/abs/0801.0551v3

Annals of Probability 2009, Vol. 37, No. 2, 687-725

Mathematics

Probability

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

Scientific paper

10.1214/08-AOP417

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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