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

Noemi Kurt

doi:10.1214/08-aop417

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arXiv · 0801.0551

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

Noemi Kurt

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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. 2009-06-11. Maximum and entropic repulsion for a Gaussian membrane model in the critical dimension. https://doi.org/10.1214/08-aop417

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