{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZTG6ZFN4Z3KEFHXXUHGUW56OU7","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":"a2729fbcfad2e8a27fc46dac8fdb94ae607092432cc9fa2f56e8f205bde120a6","cross_cats_sorted":["math.DS","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-23T06:50:58Z","title_canon_sha256":"fed00516ac0bcb12197496b307692a648920af6e270eb533d5ed037411034503"},"schema_version":"1.0","source":{"id":"1509.06859","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06859","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06859v2","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06859","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"pith_short_12","alias_value":"ZTG6ZFN4Z3KE","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZTG6ZFN4Z3KEFHXX","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZTG6ZFN4","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:d0c2f984a38879be875e1be7368fcbe6d88ec544a46d15af45464dfc0bb428c1","target":"graph","created_at":"2026-05-18T00:45:01Z","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":"We consider random walks on a non-elementary hyperbolic group endowed with a word distance. To a probability measure on the group are associated two numerical quantities, the rate of escape and the entropy. On the set of admissible probability measures whose support is contained in a given finite set, we show that both quantities depend in an analytic way on the probability measure. Our spectral techniques also give a new proof of the central limit theorem, and imply that the corresponding variance is analytic.","authors_text":"S\\'ebastien Gou\\\"ezel (LMJL)","cross_cats":["math.DS","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-23T06:50:58Z","title":"Analyticity of the entropy and the escape rate of random walks in hyperbolic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06859","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:bc473a7b85bc9111ff95003b9f8df6e337681b89b793caf9330f937a0c077ecb","target":"record","created_at":"2026-05-18T00:45:01Z","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":"a2729fbcfad2e8a27fc46dac8fdb94ae607092432cc9fa2f56e8f205bde120a6","cross_cats_sorted":["math.DS","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-23T06:50:58Z","title_canon_sha256":"fed00516ac0bcb12197496b307692a648920af6e270eb533d5ed037411034503"},"schema_version":"1.0","source":{"id":"1509.06859","kind":"arxiv","version":2}},"canonical_sha256":"cccdec95bcced4429ef7a1cd4b77cea7d93ec7881ce367f5a1fac997328b16fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cccdec95bcced4429ef7a1cd4b77cea7d93ec7881ce367f5a1fac997328b16fa","first_computed_at":"2026-05-18T00:45:01.835529Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:01.835529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GDSFQprOvtK+5YGvVlJOwB3TPiiWlZPWqrdwuBHCYfGFJwJdDo5niZVSwXadCUE0qcSl+6iGQ1jQBNi/h+wkAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:01.835925Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06859","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc473a7b85bc9111ff95003b9f8df6e337681b89b793caf9330f937a0c077ecb","sha256:d0c2f984a38879be875e1be7368fcbe6d88ec544a46d15af45464dfc0bb428c1"],"state_sha256":"65f12674e2247136919412b9b8e262329b1279a9e7e76253245fdb6e448a5ec7"}