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Fast decay of covariances under delta-pinning in the critical and supercritical membrane model

Erwin Bolthausen, Alessandra Cipriani, Noemi Kurt

7/1/16 Published in : arXiv:1601.01513

We consider the membrane model, that is the centered Gaussian field on Zd whose covariance matrix is given by the inverse of the discrete Bilaplacian. We impose a δ- pinning condition, giving a reward of strength ε for the field to be 0 at any site of the lattice. In this paper we prove that in dimensions d\geq 4 covariances of the pinned field decay at least stretched-exponentially, as opposed to the field without pinning, where the decay is polynomial in d\geq 5 and logarithmic in d=4. The proof is based on estimates for certain discrete Sobolev norms, and on a Bernoulli domination result.

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  • Statistical Mechanics

String Theory as a Higher Spin Theory

Quantum Anomalies and Logarithmic Derivatives

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