{"paper":{"title":"Edge-based mean-field approximation of dynamics on networks via approximate lumping of Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"physics.soc-ph","authors_text":"G\\'abor Tim\\'ar, Jonathan A. Ward, P\\'eter L. Simon","submitted_at":"2026-06-30T15:56:04Z","abstract_excerpt":"Mean-field approximations for dynamical processes on networks are widely used, but existing derivations often rely either on moment closures or on idealised assumptions about network structure, leaving the nature of the underlying averaging unclear. Here we present a mathematically principled framework for deriving edge-based mean-field approximations for a broad class of Markov processes on networks using approximate lumping. We consider models in which each vertex is in one of a finite number of vertex states and transitions depend on the number of neighbours in each state. Our approach part"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05425","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.05425/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}