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arXiv · 1304.6133

On Maximal Correlation, Hypercontractivity, and the Data Processing Inequality studied by Erkip and Cover

Venkat Anantharam·Amin Gohari·Sudeep Kamath·Chandra Nair
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Abstract

In this paper we provide a new geometric characterization of the Hirschfeld-Gebelein-Rényi maximal correlation of a pair of random $(X,Y)$, as well as of the chordal slope of the nontrivial boundary of the hypercontractivity ribbon of $(X,Y)$ at infinity. The new characterizations lead to simple proofs for some of the known facts about these quantities. We also provide a counterexample to a data processing inequality claimed by Erkip and Cover, and find the correct tight constant for this kind of inequality.

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Venkat Anantharam, Amin Gohari, Sudeep Kamath, Chandra Nair. 2013-04-22. On Maximal Correlation, Hypercontractivity, and the Data Processing Inequality studied by Erkip and Cover. https://arxiv.org/abs/1304.6133

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