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November 2019 $\Phi$-entropy inequalities and asymmetric covariance estimates for convex measures
Van Hoang Nguyen
Bernoulli 25(4A): 3090-3108 (November 2019). DOI: 10.3150/18-BEJ1082

Abstract

In this paper, we use the semi-group method and an adaptation of the $L^{2}$-method of Hörmander to establish some $\Phi$-entropy inequalities and asymmetric covariance estimates for the strictly convex measures in $\mathbb{R}^{n}$. These inequalities extends the ones for the strictly log-concave measures to more general setting of convex measures. The $\Phi$-entropy inequalities are turned out to be sharp in the special case of Cauchy measures. Finally, we show that the similar inequalities for log-concave measures can be obtained from our results in the limiting case.

Citation

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Van Hoang Nguyen. "$\Phi$-entropy inequalities and asymmetric covariance estimates for convex measures." Bernoulli 25 (4A) 3090 - 3108, November 2019. https://doi.org/10.3150/18-BEJ1082

Information

Received: 1 April 2018; Revised: 1 September 2018; Published: November 2019
First available in Project Euclid: 13 September 2019

zbMATH: 07110122
MathSciNet: MR4003575
Digital Object Identifier: 10.3150/18-BEJ1082

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

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Vol.25 • No. 4A • November 2019
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