{"paper":{"title":"Asymptotic Behavior of the Maximum and Minimum Singular Value of Random Vandermonde Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.PR","authors_text":"Gabriel H. Tucci, Philip A. Whiting","submitted_at":"2012-02-15T01:13:13Z","abstract_excerpt":"This work examines various statistical distributions in connection with random Vandermonde matrices and their extension to $d$--dimensional phase distributions. Upper and lower bound asymptotics for the maximum singular value are found to be $O(\\log^{1/2}{N^{d}})$ and $\\Omega((\\log N^{d} /(\\log \\log N^d))^{1/2})$ respectively where $N$ is the dimension of the matrix, generalizing the results in \\cite{TW}. We further study the behavior of the minimum singular value of these random matrices. In particular, we prove that the minimum singular value is at most $N\\exp(-C\\sqrt{N}))$ with high probabi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3184","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"}