The Annals of Probability
- Ann. Probab.
- Volume 37, Number 2 (2009), 687-725.
Maximum and entropic repulsion for a Gaussian membrane model in the critical dimension
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.
Ann. Probab., Volume 37, Number 2 (2009), 687-725.
First available in Project Euclid: 30 April 2009
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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. https://projecteuclid.org/euclid.aop/1241099926