The Annals of Probability

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

Noemi Kurt

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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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Ann. Probab., Volume 37, Number 2 (2009), 687-725.

First available in Project Euclid: 30 April 2009

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Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B41: Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41] 31B30: Biharmonic and polyharmonic equations and functions

Random interfaces membrane model entropic repulsion discrete biharmonic Green’s function


Kurt, Noemi. Maximum and entropic repulsion for a Gaussian membrane model in the critical dimension. Ann. Probab. 37 (2009), no. 2, 687--725. doi:10.1214/08-AOP417.

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