{"paper":{"title":"Volume fluctuations of random analytic varieties in the unit ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bharti Pridhnani, Xavier Massaneda","submitted_at":"2014-02-06T10:19:37Z","abstract_excerpt":"Given a Gaussian analytic function $f_L$ of intesity $L$ in the unit ball of $\\mathbb C^n$, $n\\geq 2$, consider its (random) zero variety $Z(f_L)$. We study the variance of the $(n-1)$-dimensional volume of $Z(f_L)$ inside a pseudo-hyperbolic ball of radius $r$. We first express this variance as an integral of a positive function in the unit disk. Then we study its asymptotic behaviour as $L\\to\\infty$ and as $r\\to 1^{-}$. Both the results and the proofs generalise to the ball those given by Jeremiah Buckley for the unit disk."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1302","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"}