{"paper":{"title":"Volumes of Restricted Minkowski Sums and the Free Analogue of the Entropy Power Inequality","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"D. Voiculescu, Stanislaw J. Szarek","submitted_at":"1995-10-27T00:00:00Z","abstract_excerpt":"In noncommutative probability theory independence can be based on free products instead of tensor products. This yields a highly noncommutative theory: free probability . Here we show that the classical Shannon's entropy power inequality has a counterpart for the free analogue of entropy .\n  The free entropy (introduced recently by the second named author), consistently with Boltzmann's formula $S=k\\log W$, was defined via volumes of matricial microstates. Proving the free entropy power inequality naturally becomes a geometric question.\n  Restricting the Minkowski sum of two sets means to spec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9510203","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"}