TY - JOUR

T1 - Exponential Decay of Covariances for the Supercritical Membrane Model

AU - Bolthausen, Erwin

AU - Cipriani, Alessandra

AU - Kurt, Noemi

PY - 2017/8/1

Y1 - 2017/8/1

N2 - 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≥ 5 covariances 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.

AB - 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≥ 5 covariances 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.

UR - http://www.scopus.com/inward/record.url?scp=85018795142&partnerID=8YFLogxK

U2 - 10.1007/s00220-017-2886-x

DO - 10.1007/s00220-017-2886-x

M3 - Article

AN - SCOPUS:85018795142

VL - 353

SP - 1217

EP - 1240

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -