{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:BKUGRBC5EYZBKZ7GX33BAMAPWD","short_pith_number":"pith:BKUGRBC5","schema_version":"1.0","canonical_sha256":"0aa868845d26321567e6bef610300fb0c7b21070252fc3d0ddc3fc93ef863ba5","source":{"kind":"arxiv","id":"1303.4096","version":1},"attestation_state":"computed","paper":{"title":"Median and mean of the Supremum of $L^2$ normalized random holmorphic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.PR","authors_text":"Renjie Feng, Steve Zelditch","submitted_at":"2013-03-17T20:03:21Z","abstract_excerpt":"We prove that the expected value and median of the supremum of $L^2$ normalized random holomorphic fields of degree $n$ on $m$-dimensional K\\\"ahler manifolds are asymptotically of order $\\sqrt{m\\log n}$. This improves the prior result of Shiffman-Zelditch (arXiv:math/0303335) that the upper bound of the media is of order $\\sqrt{\\log n}$\n  The estimates are based on the entropy methods of Dudley and Sudakov combined with a precise analysis of the relevant pseudo-metric and its covering numbers, which can be precisely evaluated using off-diagonal asymptotics of Bergman kernels. Recent work of th"},"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":"1303.4096","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-17T20:03:21Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"4df6ebdcdef19d72b2e838ae3ce9645841e58bf59d9ddb36d49b875c977860d2","abstract_canon_sha256":"e8d082c068cdbc99907cb64191ffa9dd97d292d01b5d5893ea264c1562c27884"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:43.174496Z","signature_b64":"UMrGGDtSyeTOBQ06Z1T7aycQqAl0oQnMT2OPbyq385m5Ne8mBIeHWCi2YeTtxoTyrKmAdJ0Zbmmfmk3CAiXEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0aa868845d26321567e6bef610300fb0c7b21070252fc3d0ddc3fc93ef863ba5","last_reissued_at":"2026-05-18T02:50:43.173723Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:43.173723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Median and mean of the Supremum of $L^2$ normalized random holmorphic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.PR","authors_text":"Renjie Feng, Steve Zelditch","submitted_at":"2013-03-17T20:03:21Z","abstract_excerpt":"We prove that the expected value and median of the supremum of $L^2$ normalized random holomorphic fields of degree $n$ on $m$-dimensional K\\\"ahler manifolds are asymptotically of order $\\sqrt{m\\log n}$. This improves the prior result of Shiffman-Zelditch (arXiv:math/0303335) that the upper bound of the media is of order $\\sqrt{\\log n}$\n  The estimates are based on the entropy methods of Dudley and Sudakov combined with a precise analysis of the relevant pseudo-metric and its covering numbers, which can be precisely evaluated using off-diagonal asymptotics of Bergman kernels. Recent work of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4096","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1303.4096","created_at":"2026-05-18T02:50:43.173849+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.4096v1","created_at":"2026-05-18T02:50:43.173849+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4096","created_at":"2026-05-18T02:50:43.173849+00:00"},{"alias_kind":"pith_short_12","alias_value":"BKUGRBC5EYZB","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"BKUGRBC5EYZBKZ7G","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"BKUGRBC5","created_at":"2026-05-18T12:27:38.830355+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BKUGRBC5EYZBKZ7GX33BAMAPWD","json":"https://pith.science/pith/BKUGRBC5EYZBKZ7GX33BAMAPWD.json","graph_json":"https://pith.science/api/pith-number/BKUGRBC5EYZBKZ7GX33BAMAPWD/graph.json","events_json":"https://pith.science/api/pith-number/BKUGRBC5EYZBKZ7GX33BAMAPWD/events.json","paper":"https://pith.science/paper/BKUGRBC5"},"agent_actions":{"view_html":"https://pith.science/pith/BKUGRBC5EYZBKZ7GX33BAMAPWD","download_json":"https://pith.science/pith/BKUGRBC5EYZBKZ7GX33BAMAPWD.json","view_paper":"https://pith.science/paper/BKUGRBC5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.4096&json=true","fetch_graph":"https://pith.science/api/pith-number/BKUGRBC5EYZBKZ7GX33BAMAPWD/graph.json","fetch_events":"https://pith.science/api/pith-number/BKUGRBC5EYZBKZ7GX33BAMAPWD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BKUGRBC5EYZBKZ7GX33BAMAPWD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BKUGRBC5EYZBKZ7GX33BAMAPWD/action/storage_attestation","attest_author":"https://pith.science/pith/BKUGRBC5EYZBKZ7GX33BAMAPWD/action/author_attestation","sign_citation":"https://pith.science/pith/BKUGRBC5EYZBKZ7GX33BAMAPWD/action/citation_signature","submit_replication":"https://pith.science/pith/BKUGRBC5EYZBKZ7GX33BAMAPWD/action/replication_record"}},"created_at":"2026-05-18T02:50:43.173849+00:00","updated_at":"2026-05-18T02:50:43.173849+00:00"}