{"paper":{"title":"Random linear systems with sparse solutions -- finite dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.PR"],"primary_cat":"math.OC","authors_text":"Mihailo Stojnic","submitted_at":"2016-12-19T20:45:24Z","abstract_excerpt":"In our companion work \\cite{Stojnicl1RegPosasymldp} we revisited random under-determined linear systems with sparse solutions. The main emphasis was on the performance analysis of the $\\ell_1$ heuristic in the so-called asymptotic regime, i.e. in the regime where the systems' dimensions are large. Through an earlier sequence of work \\cite{DonohoPol,DonohoUnsigned,StojnicCSetam09,StojnicUpper10}, it is now well known that in such a regime the $\\ell_1$ exhibits the so-called \\emph{phase transition} (PT) phenomenon. \\cite{Stojnicl1RegPosasymldp} then went much further and established the so-calle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06344","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"}