{"paper":{"title":"Distribution of the eigenvalues of a random system of homogeneous polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Paul Breiding, Peter B\\\"urgisser","submitted_at":"2015-07-09T14:55:31Z","abstract_excerpt":"Let $f=(f_1,\\ldots,f_n)$ be a system of $n$ complex homogeneous polynomials in $n$ variables of degree $d$. We call $\\lambda\\in\\mathbb{C}$ an eigenvalue of $f$ if there exists $v\\in\\mathbb{C}^n\\backslash\\{0\\}$ with $f(v)=\\lambda v$, generalizing the case of eigenvalues of matrices ($d=1$). We derive the distribution of $\\lambda$ when the $f_i$ are independently chosen at random according to the unitary invariant Weyl distribution and determine the limit distribution for $n\\to\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02539","kind":"arxiv","version":3},"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"}