Fachgebiet Mathematische Stochastik und Anwendungen in statistischer Physik und Biologie

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Exponential decay ofcovariances for the supercritical membrane model

Bolthausen, Erwin ; Cipriani, Alessandra ; Kurt, Noemi (2017)

We consider the membrane model, that is the centered Gaussian field on Zdwhose covariance matrix is given by the inverse of the discrete Bilaplacian. We impose aδ-pinning condition, giving a reward of strengthεfor the field to be 0 at any site of the lattice. In this paper we prove that in dimensionsd≥5covariances of the pinned field decay at least exponentially, as opposed to the field without...

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