{"paper":{"title":"Markov branching in the vertex splitting model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Sigurdur Orn Stefansson","submitted_at":"2011-03-17T16:01:56Z","abstract_excerpt":"We study a special case of the vertex splitting model which is a recent model of randomly growing trees. For any finite maximum vertex degree $D$, we find a one parameter model, with parameter $\\alpha \\in [0,1]$ which has a so--called Markov branching property. When $D=\\infty$ we find a two parameter model with an additional parameter $\\gamma \\in [0,1]$ which also has this feature. In the case $D = 3$, the model bears resemblance to Ford's $\\alpha$--model of phylogenetic trees and when $D=\\infty$ it is similar to its generalization, the $\\alpha\\gamma$--model. For $\\alpha = 0$, the model reduce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3445","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"}