Exponential Decay of Covariances for the Supercritical Membrane Model

Erwin Bolthausen, Alessandra Cipriani, Noemi Kurt

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1217-1240
Number of pages24
JournalCommunications in Mathematical Physics
Issue number3
Publication statusPublished - 1 Aug 2017
Externally publishedYes

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