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Journal of Theoretical Probability

, Volume 25, Issue 1, pp 92–99 | Cite as

A Gaussian Inequality for Expected Absolute Products

  • Wenbo V. Li
  • Ang Wei
Article

Abstract

We prove the inequality that \({\mathbb{E}}|X_{1}X_{2}\cdots X_{n}|\leq \sqrt{\mathrm{per}(\varSigma )}\), for any centered Gaussian random variables X 1,…,X n with the covariance matrix Σ, followed by several applications and examples. We also discuss a conjecture on the lower bound of the expectation.

Keywords

Multivariate Gaussian Permanent Wick formula MTP2 density 

Mathematics Subject Classification (2000)

60E15 62H12 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.517B Ewing Hall, Department of Mathematical SciencesUniversity of DelawareNewarkUSA
  2. 2.811 Hylan Hall, Department of MathematicsUniversity of RochesterRochesterUSA

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