{"paper":{"title":"Tail behavior of solutions of linear recursions on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mariana Olvera-Cravioto","submitted_at":"2011-08-18T18:49:46Z","abstract_excerpt":"Consider the linear nonhomogeneous fixed point equation\n  R =_d sum_{i=1}^N C_i R_i + Q, where (Q,N,C_1,...,C_N) is a random vector with N in{0,1,2,3,...}U{infty}, {C_i}_{i=1}^N >= 0, P(|Q|>0) > 0, and {R_i}_{i=1}^N is a sequence of i.i.d. random variables independent of (Q,N,C_1,...,C_N) having the same distribution as R. It is known that R will have a heavy-tailed distribution under several different sets of assumptions on the vector (Q,N,C_1,...,C_N). This paper investigates the settings where either Z_N = sum_{i=1}^N C_i or Q are regularly varying with index -alpha < -1 and E[sum_{i=1}^N C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3809","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"}