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These parameters are chosen in such a way that the rotation invariant nearest neighbor walk on $G^{(n)}$, as $n\\rightarrow\\infty$, converges to a Brown"},"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":"1311.7583","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-11-29T14:53:20Z","cross_cats_sorted":[],"title_canon_sha256":"d00a5407fb9f550a69c9578b9c8eeead81d96dbd940b351f3e38983a1b7aac26","abstract_canon_sha256":"dca3cecbdcac56be931ad8097c552a48906750ff836e3ae8d178c1ba66f84321"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:33.929355Z","signature_b64":"GNWcWobQJ4KrSPs6u3shNy/QkvZ9u6VG4gZd9MojFfr5X6ydkQzeZHU4yfLO/j2Td9A1cxqYXid05SKLlqSjAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c2d6a548449c67008cd518a972a2210f17ee172653d1aa1b7b962fb87e439d3","last_reissued_at":"2026-05-18T02:17:33.928681Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:33.928681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Loop cluster on the discrete circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yinshan Chang","submitted_at":"2013-11-29T14:53:20Z","abstract_excerpt":"The loop clusters of a Poissonian ensemble of Markov loops on a finite or countable graph have been studied in \\cite{Markovian-loop-clusters-on-graphs}. 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