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Under the limit $ N\\to\\infty $, we suitably tune the asymmetry $ (\\ell-r) $ to zero like $N^{-\\frac{1}{2}}$ and the inhomogenei"},"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":"1806.09682","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-25T19:39:51Z","cross_cats_sorted":[],"title_canon_sha256":"932fc8b0b35dc354f0a10aff225f92bf158e295cc4ee1eea7aef4a95dcded6ac","abstract_canon_sha256":"59ac09b1d1b496a37bfe2c19b3fb60b1d7ddb459f3400747a080c5a5b8e86990"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:00:11.055847Z","signature_b64":"6RERAEMxfR4LtT+XJA9XQhxbt8sVCZWVp3hfc6ozEykPGtQe30va9bfwgrYIzgr7nYbUxHrm69yJHq311cJeDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73a5bbd20de2b1ce1a2193dc6099a3e194a98e348e86f2e48031677d166a3f7a","last_reissued_at":"2026-07-05T01:00:11.055383Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:00:11.055383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"SPDE Limit of Weakly Inhomogeneous ASEP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ivan Corwin, Li-Cheng Tsai","submitted_at":"2018-06-25T19:39:51Z","abstract_excerpt":"We study ASEP in a spatially inhomogeneous environment on a torus $ \\mathbb{T}^{(N)} = \\mathbb{Z}/N\\mathbb{Z} $ of $ N $ sites. 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