{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:JQB7ZSHNVH2GONLXTRBSUH2A46","short_pith_number":"pith:JQB7ZSHN","schema_version":"1.0","canonical_sha256":"4c03fcc8eda9f46735779c432a1f40e7ada48f44f3d5ac37315b85087154e454","source":{"kind":"arxiv","id":"1506.01841","version":1},"attestation_state":"computed","paper":{"title":"On the High Energy Behavior of Nonlinear Functionals of Random Eigenfunctions on $\\mathbb S^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Maurizia Rossi","submitted_at":"2015-06-05T09:47:09Z","abstract_excerpt":"In this short survey we recollect some of the recent results on the high energy behavior (i.e., for diverging sequences of eigenvalues) of nonlinear functionals of Gaussian eigenfunctions on the $d$-dimensional sphere $\\mathbb S^d$, $d\\ge 2$. We present a quantitative Central Limit Theorem for a class of functionals whose Hermite rank is two, which includes in particular the empirical measure of excursion sets in the non-nodal case. Concerning the nodal case, we recall a CLT result for the defect on $\\mathbb S^2$. The key tools are both, the asymptotic analysis of moments of all order for Gege"},"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":"1506.01841","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-05T09:47:09Z","cross_cats_sorted":[],"title_canon_sha256":"dab0c05904ee5db3cdf5b684a67f1e178f582aea002df60cc5c0ba3f47313474","abstract_canon_sha256":"1480536632a9790d8ecba293cebb2648b9f0abb493cbee41d2e6a62e3ae0a745"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:59.096823Z","signature_b64":"c0L6gxHWVKgHx5wwyWQ30/DDLW+ODtpTbIXPqERP+rilv0IB/Xs2mFgw47zaZD8aeDSYug43P7CffNwiCqg7CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c03fcc8eda9f46735779c432a1f40e7ada48f44f3d5ac37315b85087154e454","last_reissued_at":"2026-05-18T01:55:59.096183Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:59.096183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the High Energy Behavior of Nonlinear Functionals of Random Eigenfunctions on $\\mathbb S^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Maurizia Rossi","submitted_at":"2015-06-05T09:47:09Z","abstract_excerpt":"In this short survey we recollect some of the recent results on the high energy behavior (i.e., for diverging sequences of eigenvalues) of nonlinear functionals of Gaussian eigenfunctions on the $d$-dimensional sphere $\\mathbb S^d$, $d\\ge 2$. We present a quantitative Central Limit Theorem for a class of functionals whose Hermite rank is two, which includes in particular the empirical measure of excursion sets in the non-nodal case. Concerning the nodal case, we recall a CLT result for the defect on $\\mathbb S^2$. The key tools are both, the asymptotic analysis of moments of all order for Gege"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01841","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":"1506.01841","created_at":"2026-05-18T01:55:59.096284+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.01841v1","created_at":"2026-05-18T01:55:59.096284+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01841","created_at":"2026-05-18T01:55:59.096284+00:00"},{"alias_kind":"pith_short_12","alias_value":"JQB7ZSHNVH2G","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"JQB7ZSHNVH2GONLX","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"JQB7ZSHN","created_at":"2026-05-18T12:29:27.538025+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/JQB7ZSHNVH2GONLXTRBSUH2A46","json":"https://pith.science/pith/JQB7ZSHNVH2GONLXTRBSUH2A46.json","graph_json":"https://pith.science/api/pith-number/JQB7ZSHNVH2GONLXTRBSUH2A46/graph.json","events_json":"https://pith.science/api/pith-number/JQB7ZSHNVH2GONLXTRBSUH2A46/events.json","paper":"https://pith.science/paper/JQB7ZSHN"},"agent_actions":{"view_html":"https://pith.science/pith/JQB7ZSHNVH2GONLXTRBSUH2A46","download_json":"https://pith.science/pith/JQB7ZSHNVH2GONLXTRBSUH2A46.json","view_paper":"https://pith.science/paper/JQB7ZSHN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.01841&json=true","fetch_graph":"https://pith.science/api/pith-number/JQB7ZSHNVH2GONLXTRBSUH2A46/graph.json","fetch_events":"https://pith.science/api/pith-number/JQB7ZSHNVH2GONLXTRBSUH2A46/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JQB7ZSHNVH2GONLXTRBSUH2A46/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JQB7ZSHNVH2GONLXTRBSUH2A46/action/storage_attestation","attest_author":"https://pith.science/pith/JQB7ZSHNVH2GONLXTRBSUH2A46/action/author_attestation","sign_citation":"https://pith.science/pith/JQB7ZSHNVH2GONLXTRBSUH2A46/action/citation_signature","submit_replication":"https://pith.science/pith/JQB7ZSHNVH2GONLXTRBSUH2A46/action/replication_record"}},"created_at":"2026-05-18T01:55:59.096284+00:00","updated_at":"2026-05-18T01:55:59.096284+00:00"}