{"paper":{"title":"Finding a Large Submatrix of a Gaussian Random Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.ST","physics.data-an","stat.TH"],"primary_cat":"math.PR","authors_text":"David Gamarnik, Quan Li","submitted_at":"2016-02-26T23:08:56Z","abstract_excerpt":"We consider the problem of finding a $k\\times k$ submatrix of an $n\\times n$ matrix with i.i.d. standard Gaussian entries, which has a large average entry. It was shown earlier by Bhamidi et al. that the largest average value of such a matrix is $2\\sqrt{\\log n/k}$ with high probability. In the same paper an evidence was provided that a natural greedy algorithm called Largest Average Submatrix ($\\LAS$) should produce a matrix with average entry approximately $\\sqrt{2}$ smaller.\n  In this paper we show that the matrix produced by the $\\LAS$ algorithm is indeed $\\sqrt{2\\log n/k}$ w.h.p. Then by d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08529","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"}