{"paper":{"title":"Simulation of Random Variables under R\\'enyi Divergence Measures of All Orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Lei Yu, Vincent Y. F. Tan","submitted_at":"2018-05-31T13:10:40Z","abstract_excerpt":"The random variable simulation problem consists in using a $k$-dimensional i.i.d. random vector $X^{k}$ with distribution $P_{X}^{k}$ to simulate an $n$-dimensional i.i.d. random vector $Y^{n}$ so that its distribution is approximately $Q_{Y}^{n}$. In contrast to previous works, in this paper we consider the standard R\\'enyi divergence and two variants of all orders to measure the level of approximation. These two variants are the max-R\\'enyi divergence $D_{\\alpha}^{\\mathsf{max}}(P,Q)$ and the sum-R\\'enyi divergence $D_{\\alpha}^{+}(P,Q)$. When $\\alpha=\\infty$, these two measures are strong bec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.12451","kind":"arxiv","version":4},"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"}