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

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.

preprint2013arXivOpen access
Venkat AnantharamAmin GohariSudeep KamathChandra Nair
math.ITInformation Theory
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Venkat AnantharamAmin GohariSudeep KamathChandra Nair

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