{"paper":{"title":"Phi-Entropic Measures of Correlation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Amin Gohari, Salman Beigi","submitted_at":"2016-11-04T11:39:35Z","abstract_excerpt":"A measure of correlation is said to have the tensorization property if it is unchanged when computed for i.i.d.\\ copies. More precisely, a measure of correlation between two random variables $(X, Y)$ denoted by $\\rho(X, Y)$, has the tensorization property if $\\rho(X^n, Y^n)=\\rho(X, Y)$ where $(X^n, Y^n)$ is $n$ i.i.d.\\ copies of $(X, Y)$.Two well-known examples of such measures are the maximal correlation and the hypercontractivity ribbon (HC~ribbon). We show that the maximal correlation and HC ribbons are special cases of $\\Phi$-ribbon, defined in this paper for any function $\\Phi$ from a cla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01335","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"}