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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1402.1302","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-02-06T10:19:37Z","cross_cats_sorted":[],"title_canon_sha256":"c79cd208d29308d88e6104aadd810d7f65de2a797d40a8ca6f07fa5c92b40284","abstract_canon_sha256":"708419f80352dc41eafac3ff11a3a9a5f550736da51d389510eae29397f59cb8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:59:59.535333Z","signature_b64":"DtHJ9hHXVhYNHikafCagJmUm8IQN2Xr5jQnkpjLTiNAeASoI7pPu7xW0W0ABKNwE67Qr6u25Z/tdTtNbCpkIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24af179fc2711606e5fb8c40ac85ce36709d2793e4bf6a3d946647f8a768ec7b","last_reissued_at":"2026-05-18T02:59:59.534574Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:59:59.534574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $Z(f_L)$. 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