{"paper":{"title":"Circular law for the sum of random permutation matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Anirban Basak, Nicholas Cook, Ofer Zeitouni","submitted_at":"2017-05-25T05:37:01Z","abstract_excerpt":"Let $P_n^1,\\dots, P_n^d$ be $n\\times n$ permutation matrices drawn independently and uniformly at random, and set $S_n^d:=\\sum_{\\ell=1}^d P_n^\\ell$. We show that if $\\log^{12}n/(\\log \\log n)^{4} \\le d=O(n)$, then the empirical spectral distribution of $S_n^d/\\sqrt{d}$ converges weakly to the circular law in probability as $n \\to \\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09053","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"}