{"paper":{"title":"On Maximal Correlation, Hypercontractivity, and the Data Processing Inequality studied by Erkip and Cover","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Amin Gohari, Chandra Nair, Sudeep Kamath, Venkat Anantharam","submitted_at":"2013-04-22T23:18:28Z","abstract_excerpt":"In this paper we provide a new geometric characterization of the Hirschfeld-Gebelein-R\\'{e}nyi 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6133","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}