{"paper":{"title":"Space-Entropy Lower Bounds for Random Sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.IT","math.IT","math.PR"],"primary_cat":"cs.CC","authors_text":"Feras A. Saad, Thomas L. Draper","submitted_at":"2026-07-16T02:37:38Z","abstract_excerpt":"We prove fundamental space lower bounds for exact random sampling using an entropy source of i.i.d. uniform bits. A classic result from information theory shows that generating $n$ discrete random variables $X_1, \\dots, X_n$ requires at least $H(X_1, \\dots, X_n)$ input random bits on average, where $H$ is the Shannon entropy function. How much space must a random sampling algorithm use in order to approach this information-theoretically optimal entropy bound?\n  We prove that any random sampling algorithm that is exact for arbitrary discrete target distributions and consumes at most $H(X_1,\\ldo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14503","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.14503/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}