{"paper":{"title":"Maximums on Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mariana Olvera-Cravioto, Predrag R. Jelenkovic","submitted_at":"2014-05-24T03:56:10Z","abstract_excerpt":"We study the minimal/endogenous solution $R$ to the maximum recursion on weighted branching trees given by $$R\\stackrel{\\mathcal{D}}{=}\\left(\\bigvee_{i=1}^NC_iR_i \\right)\\vee Q,$$ where $(Q,N,C_1,C_2,\\dots)$ is a random vector with $N\\in \\mathbb{N}\\cup\\{\\infty\\}$, $P(|Q|>0)>0$ and nonnegative weights $\\{C_i\\}$, and $\\{R_i\\}_{i\\in\\mathbb{N}}$ is a sequence of i.i.d. copies of $R$ independent of $(Q,N,C_1,C_2,\\dots)$; $\\stackrel{\\mathcal{D}}{=}$ denotes equality in distribution. Furthermore, when $Q>0$ this recursion can be transformed into its additive equivalent, which corresponds to the maxim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6265","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"}