{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2UJE5FJW5NJX3IYYOOSEMDUX47","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"00a5db68ec20a606a1ea931d62fe36568a89f842cc3f8d9a97015e887e7405f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-26T19:04:35Z","title_canon_sha256":"187174484214a68bba605b46aa18f6cd2bfcfa354b080680fd5faf9e9078f9f0"},"schema_version":"1.0","source":{"id":"1302.6539","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6539","created_at":"2026-05-18T03:32:28Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6539v1","created_at":"2026-05-18T03:32:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6539","created_at":"2026-05-18T03:32:28Z"},{"alias_kind":"pith_short_12","alias_value":"2UJE5FJW5NJX","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2UJE5FJW5NJX3IYY","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2UJE5FJW","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:d1c745ea8caf67d9e1f24821a611a66e75f1c513ddacd99bb4d39e66c4436005","target":"graph","created_at":"2026-05-18T03:32:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $U$ be a Haar distributed matrix in $\\mathbb U(n)$ or $\\mathbb O (n)$. In a previous paper, we proved that after centering, the two-parameter process \\[T^{(n)} (s,t) = \\sum_{i \\leq \\lfloor ns \\rfloor, j \\leq \\lfloor nt\\rfloor} |U_{ij}|^2\\] converges in distribution to the bivariate tied-down Brownian bridge. In the present paper, we replace the deterministic truncation of $U$ by a random one, where each row (resp. column) is chosen with probability $s$ (resp. $t$) independently. We prove that the corresponding two-parameter process, after centering and normalization by $n^{-1/2}$ converges","authors_text":"Alain Rouault (LM-Versailles), Catherine Donati-Martin (LM-Versailles)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-26T19:04:35Z","title":"Random truncations of Haar distributed matrices and bridges"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6539","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2f94f548f9fd6b262fcb2d887f7108f479ee6b10a88cf75a15a6288524131c21","target":"record","created_at":"2026-05-18T03:32:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"00a5db68ec20a606a1ea931d62fe36568a89f842cc3f8d9a97015e887e7405f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-26T19:04:35Z","title_canon_sha256":"187174484214a68bba605b46aa18f6cd2bfcfa354b080680fd5faf9e9078f9f0"},"schema_version":"1.0","source":{"id":"1302.6539","kind":"arxiv","version":1}},"canonical_sha256":"d5124e9536eb537da31873a4460e97e7c4ac228638c49aa37b9dbb30b42bc3a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5124e9536eb537da31873a4460e97e7c4ac228638c49aa37b9dbb30b42bc3a3","first_computed_at":"2026-05-18T03:32:28.949767Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:28.949767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n9HfMXLxzrwSDKRLx5h1jIkld4qWxtsAxQebWQtAPO9OGhA6j8Chve6fXIQFW4p0DgKcxQIDj9904qsuOzTnBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:28.950265Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.6539","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f94f548f9fd6b262fcb2d887f7108f479ee6b10a88cf75a15a6288524131c21","sha256:d1c745ea8caf67d9e1f24821a611a66e75f1c513ddacd99bb4d39e66c4436005"],"state_sha256":"285a0dfb6dfefa02faa2d0909272e7bd6684ac151c1a83576b58e02e485af4b8"}