{"paper":{"title":"Exponential Rank Bounds for Random Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Achintya Raya Polavarapu","submitted_at":"2026-06-23T21:53:58Z","abstract_excerpt":"Fix $b\\in(0,1)$, let $1\\leq k\\leq n$, and let $A=(A_{ij})$ be an $n\\times n$ random matrix with independent real entries satisfying $$ \\sup_{x\\in\\mathbb{R}}\\mathbb{P}\\{A_{ij}=x\\}\\leq b<1 \\qquad (1\\leq i,j\\leq n). $$ We show that there exists $c>0$ such that $$ \\mathbb{P}\\{\\operatorname{rank} A\\leq n-k\\}\\leq \\exp(-cnk), \\qquad 1\\leq k\\leq n. $$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25204","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/2606.25204/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"}