{"paper":{"title":"Equidistribution of zeros of random holomorphic sections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.PR"],"primary_cat":"math.CV","authors_text":"Turgay Bayraktar","submitted_at":"2013-12-03T20:55:35Z","abstract_excerpt":"We study asymptotic distribution of zeros of random holomorphic sections of high powers of positive line bundles defined over projective homogenous manifolds. We work with a wide class of distributions that includes real and complex Gaussians. As a special case, we obtain asymptotic zero distribution of multivariate complex polynomials given by linear combinations of orthogonal polynomials with i.i.d. random coefficients. Namely, we prove that normalized zero measures of m i.i.d random polynomials, orthonormalized on a regular compact set $K\\subset \\Bbb{C}^m,$ are almost surely asymptotic to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0933","kind":"arxiv","version":4},"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"}