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Main Title: Exponential decay ofcovariances for the supercritical membrane model
Author(s): Bolthausen, Erwin
Cipriani, Alessandra
Kurt, Noemi
Type: Article
Language Code: en
Abstract: 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 pinning, where the decay is polynomial. The proof is based on estimates for certain discrete weighted norms, a percolation argument and on a Bernoulli domination result.
Issue Date: 2017
Date Available: 29-Aug-2017
DDC Class: 510 Mathematik
Journal Title: Communications in mathematical physics
Publisher: Springer
Publisher Place: Berlin, Heidelberg
Volume: 353
Issue: 3
Publisher DOI: 10.1007/s00220-017-2886-x
Page Start: 1217
Page End: 1240
EISSN: 1432-0916
ISSN: 0010-3616
Appears in Collections:FG Mathematische Stochastik und Anwendungen in statistischer Physik und Biologie » Publications

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