{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YBFVBLTXFT273RLZT6JTXPB2HK","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":"0adb4ec20f8d19ab01912c74b60a2b13bff93717b70647cd72f4a2be231b7622","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-27T21:59:21Z","title_canon_sha256":"702641027a819c2744682997f261f14c801c38c879e2b41b6e4228d8a94ce322"},"schema_version":"1.0","source":{"id":"1109.6050","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6050","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6050v2","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6050","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"pith_short_12","alias_value":"YBFVBLTXFT27","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YBFVBLTXFT273RLZ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YBFVBLTX","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:65d87f049c79dd7e6220d1c4dbcc77a141e2fd138f4933567a4cd3f5b115fe7b","target":"graph","created_at":"2026-05-18T04:02:25Z","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":"In this paper we extend the results of the research started by the first author, in which Karlin-McGregor diagonalization of certain reversible Markov chains over countably infinite general state spaces by orthogonal polynomials was used to estimate the rate of convergence to a stationary distribution.\n  We use a method of Koornwinder to generate a large and interesting family of random walks which exhibits a lack of spectral gap, and a polynomial rate of convergence to the stationary distribution. For the Chebyshev type subfamily of Markov chains, we use asymptotic techniques to obtain an upp","authors_text":"Nicholas Michalowski, Yevgeniy Kovchegov","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-27T21:59:21Z","title":"A Class of Markov Chains with no Spectral Gap"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6050","kind":"arxiv","version":2},"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":"sha256:5300b09ba407a121bdeead382789cb828af640fe2b8ac054ddab8917a2ab78b8","target":"record","created_at":"2026-05-18T04:02:25Z","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":"0adb4ec20f8d19ab01912c74b60a2b13bff93717b70647cd72f4a2be231b7622","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-27T21:59:21Z","title_canon_sha256":"702641027a819c2744682997f261f14c801c38c879e2b41b6e4228d8a94ce322"},"schema_version":"1.0","source":{"id":"1109.6050","kind":"arxiv","version":2}},"canonical_sha256":"c04b50ae772cf5fdc5799f933bbc3a3a90c38137f198b0d5e1fbd307d9462602","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c04b50ae772cf5fdc5799f933bbc3a3a90c38137f198b0d5e1fbd307d9462602","first_computed_at":"2026-05-18T04:02:25.100647Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:25.100647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"icr+2F626im4Ib9XInq0pLHsMsqBAzTlvySKkXoJqmiKocUVdSUyG9UEIk70f+zqUAgQjeeD7cCLNjKrpCnrDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:25.101167Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.6050","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5300b09ba407a121bdeead382789cb828af640fe2b8ac054ddab8917a2ab78b8","sha256:65d87f049c79dd7e6220d1c4dbcc77a141e2fd138f4933567a4cd3f5b115fe7b"],"state_sha256":"3a4ca1fae39ad74c7b5f172b72ac18acdb4922cb17d88aabb96c57d5df0a9f14"}