A Brascamp-Lieb type covariance estimate
Probability
2014-02-24 v1
Abstract
In this article, we derive a new covariance estimate. The estimate has a similar structure as the Brascamp-Lieb inequality and is optimal for ferromagnetic Gaussian measures. It can be naturally applied to deduce decay of correlations of lattice systems of continuous spins. We also discuss the relation of the new estimate with known estimates like a weighted estimate due to Helffer & Ledoux. The main ingredient of the proof of the new estimate is a directional Poincar\'e inequality which seems to be unknown.
Cite
@article{arxiv.1402.5160,
title = {A Brascamp-Lieb type covariance estimate},
author = {Georg Menz},
journal= {arXiv preprint arXiv:1402.5160},
year = {2014}
}
Comments
19 pages. arXiv admin note: substantial text overlap with arXiv:1309.0862