{"paper":{"title":"Cayley Trees and Bethe Lattices, a concise analysis for mathematicians and physicists","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Massimo Ostilli","submitted_at":"2011-09-30T06:43:53Z","abstract_excerpt":"We review critically the concepts and the applications of Cayley Trees and Bethe Lattices in statistical mechanics in a tentative effort to remove widespread misuse of these simple, but yet important - and different - ideal graphs. We illustrate, in particular, two rigorous techniques to deal with Bethe Lattices, based respectively on self-similarity and on the Kolmogorov consistency theorem, linking the latter with the Cavity and Belief Propagation methods, more known to the physics community."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6725","kind":"arxiv","version":2},"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"}