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We prove that the renormalized self-intersection local time\\ell=\\int_0^T\\int_0^t\\delta(B_t^H-B_s^H) ds dt -E\\biggl(\\int_0^T\\int_0^t\\delta (B_t^H-B_s^H) ds dt\\biggr) exists in L^2 if and only if H<3/(2d), which generalizes the Varadhan renormalization theorem to any dimension and with any Hurst parameter. Motivated by a result of Yor, we show that in the case 3/4>H\\geq\\frac{3}{2d}, r(\\epsilon)\\ell_{\\epsilon} converges in distribution to a normal law N(0,T\\sigma^2), as \\epsilon tends to zero, w"},"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":"math/0506592","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2005-06-29T10:35:28Z","cross_cats_sorted":[],"title_canon_sha256":"4f2d22701ebde68f16d918b8529fb9b3e3078cff07ff1bd90ec2fda19dccf7d1","abstract_canon_sha256":"489267ef54aa2d4a7a5d0273aa58d04b0905f2334940281f2dabc0c0e7adea4d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:40:11.375572Z","signature_b64":"9XXQBbvVbxxQTr+1qzrOe36r5qWJZ1nwCrVtEy26GIQHDG94e/+C8pWxK+s2V/Tqmr0XfxQg9vVlQ4zAYl/lAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d468b980323cd543c369b49c50eb93679d2231930a567550a8791f3415249fa9","last_reissued_at":"2026-07-04T14:40:11.375167Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:40:11.375167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Renormalized self-intersection local time for fractional Brownian motion","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Nualart, Yaozhong Hu","submitted_at":"2005-06-29T10:35:28Z","abstract_excerpt":"Let B_t^H be a d-dimensional fractional Brownian motion with Hurst parameter H\\in(0,1). Assume d\\geq2. We prove that the renormalized self-intersection local time\\ell=\\int_0^T\\int_0^t\\delta(B_t^H-B_s^H) ds dt -E\\biggl(\\int_0^T\\int_0^t\\delta (B_t^H-B_s^H) ds dt\\biggr) exists in L^2 if and only if H<3/(2d), which generalizes the Varadhan renormalization theorem to any dimension and with any Hurst parameter. Motivated by a result of Yor, we show that in the case 3/4>H\\geq\\frac{3}{2d}, r(\\epsilon)\\ell_{\\epsilon} converges in distribution to a normal law N(0,T\\sigma^2), as \\epsilon tends to zero, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506592","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0506592/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"math/0506592","created_at":"2026-07-04T14:40:11.375226+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0506592v1","created_at":"2026-07-04T14:40:11.375226+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0506592","created_at":"2026-07-04T14:40:11.375226+00:00"},{"alias_kind":"pith_short_12","alias_value":"2RULTABSHTKU","created_at":"2026-07-04T14:40:11.375226+00:00"},{"alias_kind":"pith_short_16","alias_value":"2RULTABSHTKUHQ3J","created_at":"2026-07-04T14:40:11.375226+00:00"},{"alias_kind":"pith_short_8","alias_value":"2RULTABS","created_at":"2026-07-04T14:40:11.375226+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/2RULTABSHTKUHQ3JWSOFB24TM6","json":"https://pith.science/pith/2RULTABSHTKUHQ3JWSOFB24TM6.json","graph_json":"https://pith.science/api/pith-number/2RULTABSHTKUHQ3JWSOFB24TM6/graph.json","events_json":"https://pith.science/api/pith-number/2RULTABSHTKUHQ3JWSOFB24TM6/events.json","paper":"https://pith.science/paper/2RULTABS"},"agent_actions":{"view_html":"https://pith.science/pith/2RULTABSHTKUHQ3JWSOFB24TM6","download_json":"https://pith.science/pith/2RULTABSHTKUHQ3JWSOFB24TM6.json","view_paper":"https://pith.science/paper/2RULTABS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0506592&json=true","fetch_graph":"https://pith.science/api/pith-number/2RULTABSHTKUHQ3JWSOFB24TM6/graph.json","fetch_events":"https://pith.science/api/pith-number/2RULTABSHTKUHQ3JWSOFB24TM6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2RULTABSHTKUHQ3JWSOFB24TM6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2RULTABSHTKUHQ3JWSOFB24TM6/action/storage_attestation","attest_author":"https://pith.science/pith/2RULTABSHTKUHQ3JWSOFB24TM6/action/author_attestation","sign_citation":"https://pith.science/pith/2RULTABSHTKUHQ3JWSOFB24TM6/action/citation_signature","submit_replication":"https://pith.science/pith/2RULTABSHTKUHQ3JWSOFB24TM6/action/replication_record"}},"created_at":"2026-07-04T14:40:11.375226+00:00","updated_at":"2026-07-04T14:40:11.375226+00:00"}