On Maximal Correlation, Hypercontractivity, and the Data Processing Inequality studied by Erkip and Cover
作者： Venkat Anantharam , Amin Aminzadeh Gohari , Sudeep Kamath , Chandra Nair
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摘要: In this paper we provide a new geometric characterization of the Hirschfeld-Gebelein-R\'{e}nyi maximal correlation pair random $(X,Y)$, as well chordal slope nontrivial boundary hypercontractivity ribbon $(X,Y)$ at infinity. The characterizations lead to simple proofs for some known facts about these quantities. We also counterexample data processing inequality claimed by Erkip and Cover, find correct tight constant kind inequality.
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