{"paper":{"title":"A Markovian growth dynamics on rooted binary trees evolving according to the Gompertz curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","q-bio.QM","stat.OT"],"primary_cat":"q-bio.CB","authors_text":"B. F. Svaiter, C. Landim, R. D. Portugal","submitted_at":"2008-07-10T22:00:46Z","abstract_excerpt":"Inspired by biological dynamics, we consider a growth Markov process taking values on the space of rooted binary trees, similar to the Aldous-Shields model. Fix $n\\ge 1$ and $\\beta>0$. We start at time 0 with the tree composed of a root only. At any time, each node with no descendants, independently from the other nodes, produces two successors at rate $\\beta(n-k)/n$, where $k$ is the distance from the node to the root. Denote by $Z_n(t)$ the number of nodes with no descendants at time $t$ and let $T_n = \\beta^{-1} n \\ln(n /\\ln 4) + (\\ln 2)/(2 \\beta)$. We prove that $2^{-n} Z_n(T_n + n \\tau)$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.1750","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"}