{"paper":{"title":"Exchangeable Markov processes on graphs: Feller case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Harry Crane","submitted_at":"2015-09-22T17:57:28Z","abstract_excerpt":"The transition law of every exchangeable Feller process on the space of countable graphs is determined by a $\\sigma$-finite measure on the space of $\\{0,1\\}\\times\\{0,1\\}$-valued arrays. In discrete-time, this characterization amounts to a construction from an independent, identically distributed sequence of exchangeable random functions. In continuous-time, the behavior is enriched by a L\\'evy--It\\^o-type decomposition of the jump measure into mutually singular components that govern global, vertex-level, and edge-level dynamics. Furthermore, every such process almost surely projects to a Fell"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06701","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":""},"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"}