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2014 A Brascamp-Lieb type covariance estimate
Georg Menz
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Electron. J. Probab. 19: 1-15 (2014). DOI: 10.1214/EJP.v19-2997

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 ingredi.ent of the proof of the new estimate is a directional Poincaré inequality which seems to be unknown.

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Georg Menz. "A Brascamp-Lieb type covariance estimate." Electron. J. Probab. 19 1 - 15, 2014. https://doi.org/10.1214/EJP.v19-2997

Information

Accepted: 30 August 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1302.82026
MathSciNet: MR3256878
Digital Object Identifier: 10.1214/EJP.v19-2997

Subjects:
Primary: 82B20
Secondary: 60K35 , 82C26

Keywords: Brascamp-Lieb , continuous spin , decay of correlations , lattice systems

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Vol.19 • 2014
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