{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PBDYT43FWSIAPEMUC35LB3CGOS","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":"682d1b850a8012a99d02ad142409591edc3c77fa10413bd583b4bb8166014925","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-22T14:06:32Z","title_canon_sha256":"bfa2dd3899b902645a0a2ef269c8cfd11870c280ac6ffc502d7dbfa60ff5f3c8"},"schema_version":"1.0","source":{"id":"1604.06664","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06664","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06664v1","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06664","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"pith_short_12","alias_value":"PBDYT43FWSIA","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PBDYT43FWSIAPEMU","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PBDYT43F","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:a926a45ccf8c5df301f0d62c3773da4f2eb73357e0892e29ba9f382eb764373d","target":"graph","created_at":"2026-05-18T01:16:28Z","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":"This paper considers the optimal scaling problem for high-dimensional random walk Metropolis algorithms for densities which are differentiable in Lp mean but which may be irregular at some points (like the Laplace density for example) and/or are supported on an interval. Our main result is the weak convergence of the Markov chain (appropriately rescaled in time and space) to a Langevin diffusion process as the dimension d goes to infinity. Because the log-density might be non-differentiable, the limiting diffusion could be singular. The scaling limit is established under assumptions which are ","authors_text":"Alain Durmus (LTCI), Eric Moulines (CMAP), Gareth O. Roberts, Sylvain Le Corff","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-22T14:06:32Z","title":"Optimal scaling of the Random Walk Metropolis algorithm under Lp mean differentiability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06664","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:f04214d0b50d837b94530e45b7a3f60c8afc92fbcfce11ed9f9185d812bc0a64","target":"record","created_at":"2026-05-18T01:16:28Z","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":"682d1b850a8012a99d02ad142409591edc3c77fa10413bd583b4bb8166014925","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-22T14:06:32Z","title_canon_sha256":"bfa2dd3899b902645a0a2ef269c8cfd11870c280ac6ffc502d7dbfa60ff5f3c8"},"schema_version":"1.0","source":{"id":"1604.06664","kind":"arxiv","version":1}},"canonical_sha256":"784789f365b49007919416fab0ec4674b85c2458ba59b34b80e860a529b1b2c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"784789f365b49007919416fab0ec4674b85c2458ba59b34b80e860a529b1b2c9","first_computed_at":"2026-05-18T01:16:28.477898Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:28.477898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7g5Za3q13HMbDGDiuizb4FPblPOkFPUxWbTQs218Kp70OaQRjFks96NzgEQZXq6rhE1YcsLv88PElJWcqq4zDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:28.478577Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06664","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f04214d0b50d837b94530e45b7a3f60c8afc92fbcfce11ed9f9185d812bc0a64","sha256:a926a45ccf8c5df301f0d62c3773da4f2eb73357e0892e29ba9f382eb764373d"],"state_sha256":"09c6a8ec9ebe3e70a23fe070d9c20ba0185fa32f2eec8845c892e34dec324788"}