New Connections Between the Entropy Power Inequality and Geometric Inequalities
New Connections Between the Entropy Power Inequality and Geometric Inequalities
复制标题
熵幂不等式与几何不等式之间的新联系
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
V. Kostina
中科院分区：
文献类型：
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作者：
Arnaud Marsiglietti;V. Kostina
熵幂不等式（EPI）在信息论中有着重要的地位，它与著名的几何不等式有着密切的联系。特别是，它经常被比作凸几何中的Brunn-Minkowski不等式。本文进一步加强了EPI与几何不等式之间的联系。具体来说，我们建立了一个强形式的反向EPI和超平面猜想，这是一个长期存在的猜想在高维凸几何之间的等价性。我们还提供了一个简单的证明超平面猜想的某一类分布，作为一个简单的后果EPI。
The entropy power inequality (EPI) has a fundamental role in Information Theory, and has deep connections with famous geometric inequalities. In particular, it is often compared to the Brunn-Minkowski inequality in convex geometry. In this article, we further strengthen the relationships between the EPI and geometric inequalities. Specifically, we establish an equivalence between a strong form of reverse EPI and the hyperplane conjecture, which is a long-standing conjecture in high-dimensional convex geometry. We also provide a simple proof of the hyperplane conjecture for a certain class of distributions, as a straightforward consequence of the EPI.