A Brascamp-Lieb type covariance estimate

Georg Menz

doi:10.1214/EJP.v19-2997

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Home > Journals > Electron. J. Probab. > Volume 19 > Article

2014 A Brascamp-Lieb type covariance estimate

Georg Menz

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Georg Menz¹
¹Stanford University

Electron. J. Probab. 19: 1-15 (2014). DOI: 10.1214/EJP.v19-2997

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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.