{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:352K65QQNZQXFMXJ3UPUBAV7AZ","short_pith_number":"pith:352K65QQ","schema_version":"1.0","canonical_sha256":"df74af76106e6172b2e9dd1f4082bf067225185233ff05820b9e02f168233fb9","source":{"kind":"arxiv","id":"1312.2863","version":1},"attestation_state":"computed","paper":{"title":"Extremes of homogeneous Gaussian random fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enkelejd Hashorva, Krzysztof D\\k{e}bicki, Natalia Soja-Kukie{\\l}a","submitted_at":"2013-12-10T16:37:02Z","abstract_excerpt":"Let $\\{X(s,t):s,t\\geqslant 0\\}$ be a centered homogeneous Gaussian field with a.s. continuous sample paths and correlation function $r(s,t)=Cov(X(s,t),X(0,0))$ such that \\[r(s,t)=1-|s|^{\\alpha_1}-|t|^{\\alpha_2}+o(|s|^{\\alpha_1}+|t|^{\\alpha_2}), \\quad s,t \\to 0,\\] with $\\alpha_1,\\alpha_2\\in(0,2],$ and $r(s,t)<1$ for $(s,t)\\neq(0,0)$. In this contribution we derive an exact asymptotic expansion (as $u\\to \\infty$) of $$\\mathbb{P}\\left(\\sup_{(s n_1(u),t n_2(u))\\in\\left[0,x\\right]\\times\\left[0,y\\right]}X(s,t)\\leqslant u\\right),$$ where $n_1(u)n_2(u)=u^{2/\\alpha_1+2/\\alpha_2}\\Psi(u)$, which holds un"},"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":"1312.2863","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-10T16:37:02Z","cross_cats_sorted":[],"title_canon_sha256":"569657ef802ed4f2f9aa480643f7847064b03d5ac1d3af6aef414562d95bec26","abstract_canon_sha256":"083a17420c354e3343bd13a2f2a7ae045c5dadf148d654c3bea34c461c4bd6aa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:08.231777Z","signature_b64":"/PwOQXarIkuOBBWGCkbHd+cCIfrC19NGjDtAx3/COQDpWEDFp6Dm56bfY+bvSlhNugQGXo1VAAroOzSIxwUCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df74af76106e6172b2e9dd1f4082bf067225185233ff05820b9e02f168233fb9","last_reissued_at":"2026-05-18T03:05:08.231207Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:08.231207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremes of homogeneous Gaussian random fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enkelejd Hashorva, Krzysztof D\\k{e}bicki, Natalia Soja-Kukie{\\l}a","submitted_at":"2013-12-10T16:37:02Z","abstract_excerpt":"Let $\\{X(s,t):s,t\\geqslant 0\\}$ be a centered homogeneous Gaussian field with a.s. continuous sample paths and correlation function $r(s,t)=Cov(X(s,t),X(0,0))$ such that \\[r(s,t)=1-|s|^{\\alpha_1}-|t|^{\\alpha_2}+o(|s|^{\\alpha_1}+|t|^{\\alpha_2}), \\quad s,t \\to 0,\\] with $\\alpha_1,\\alpha_2\\in(0,2],$ and $r(s,t)<1$ for $(s,t)\\neq(0,0)$. In this contribution we derive an exact asymptotic expansion (as $u\\to \\infty$) of $$\\mathbb{P}\\left(\\sup_{(s n_1(u),t n_2(u))\\in\\left[0,x\\right]\\times\\left[0,y\\right]}X(s,t)\\leqslant u\\right),$$ where $n_1(u)n_2(u)=u^{2/\\alpha_1+2/\\alpha_2}\\Psi(u)$, which holds un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2863","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":"1312.2863","created_at":"2026-05-18T03:05:08.231289+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.2863v1","created_at":"2026-05-18T03:05:08.231289+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2863","created_at":"2026-05-18T03:05:08.231289+00:00"},{"alias_kind":"pith_short_12","alias_value":"352K65QQNZQX","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"352K65QQNZQXFMXJ","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"352K65QQ","created_at":"2026-05-18T12:27:32.513160+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/352K65QQNZQXFMXJ3UPUBAV7AZ","json":"https://pith.science/pith/352K65QQNZQXFMXJ3UPUBAV7AZ.json","graph_json":"https://pith.science/api/pith-number/352K65QQNZQXFMXJ3UPUBAV7AZ/graph.json","events_json":"https://pith.science/api/pith-number/352K65QQNZQXFMXJ3UPUBAV7AZ/events.json","paper":"https://pith.science/paper/352K65QQ"},"agent_actions":{"view_html":"https://pith.science/pith/352K65QQNZQXFMXJ3UPUBAV7AZ","download_json":"https://pith.science/pith/352K65QQNZQXFMXJ3UPUBAV7AZ.json","view_paper":"https://pith.science/paper/352K65QQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.2863&json=true","fetch_graph":"https://pith.science/api/pith-number/352K65QQNZQXFMXJ3UPUBAV7AZ/graph.json","fetch_events":"https://pith.science/api/pith-number/352K65QQNZQXFMXJ3UPUBAV7AZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/352K65QQNZQXFMXJ3UPUBAV7AZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/352K65QQNZQXFMXJ3UPUBAV7AZ/action/storage_attestation","attest_author":"https://pith.science/pith/352K65QQNZQXFMXJ3UPUBAV7AZ/action/author_attestation","sign_citation":"https://pith.science/pith/352K65QQNZQXFMXJ3UPUBAV7AZ/action/citation_signature","submit_replication":"https://pith.science/pith/352K65QQNZQXFMXJ3UPUBAV7AZ/action/replication_record"}},"created_at":"2026-05-18T03:05:08.231289+00:00","updated_at":"2026-05-18T03:05:08.231289+00:00"}