{"paper":{"title":"Stochastic domination for iterated convolutions and catalytic majorization","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"quant-ph","authors_text":"Guillaume Aubrun (ICJ), Ion Nechita (ICJ)","submitted_at":"2007-07-02T12:44:14Z","abstract_excerpt":"We study how iterated convolutions of probability measures compare under stochastic domination. We give necessary and sufficient conditions for the existence of an integer $n$ such that $\\mu^{*n}$ is stochastically dominated by $\\nu^{*n}$ for two given probability measures $\\mu$ and $\\nu$. As a consequence we obtain a similar theorem on the majorization order for vectors in $\\R^d$. In particular we prove results about catalysis in quantum information theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.0211","kind":"arxiv","version":2},"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"}