{"paper":{"title":"Permanents of heavy-tailed random matrices with positive elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ton\\'ci Antunovi\\'c","submitted_at":"2011-11-15T08:59:43Z","abstract_excerpt":"We study the asymptotic behavior of permanents of $n \\times n$ random matrices $A$ with positive entries. We assume that $A$ has either i.i.d. entries or is a symmetric matrix with the i.i.d. upper triangle. Under the assumption that elements have power law decaying tails, we prove a strong law of large numbers for $\\log \\perm A$. We calculate the values of the limit $\\lim_{n \\to \\infty}\\frac{\\log \\perm A}{n \\log n}$ in terms of the exponent of the power law distribution decay, and observe a first order phase transition in the limit as the mean becomes infinite. The methods extend to a wide cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3454","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"}