Exponential decay of covariances for the supercritical membrane model
| Autor: | Erwin Bolthausen, Alessandra Cipriani, Noemi Kurt |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
39A12
Gaussian 82B41 Inverse 31B30 01 natural sciences bilaplacian membrane model 010104 statistics & probability symbols.namesake Bernoulli's principle Exponential growth Lattice (order) FOS: Mathematics pinning 0101 mathematics Exponential decay Mathematical Physics Mathematics Covariance matrix 010102 general mathematics Mathematical analysis Probability (math.PR) Statistical and Nonlinear Physics Supercritical fluid 60K37 60K35 decay of covariances symbols Mathematics - Probability |
| DOI: | 10.48550/arxiv.1609.04258 |
| Popis: | We consider the membrane model, that is the centered Gaussian field on $\mathbb Z^d$ whose covariance matrix is given by the inverse of the discrete Bilaplacian. We impose a $\delta-$pinning condition, giving a reward of strength $\varepsilon$ for the field to be $0$ at any site of the lattice. In this paper we prove that in dimensions $d\geq 5$ 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. Comment: 23 pages, 2 figures. Comments are welcome |
| Databáze: | OpenAIRE |
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