{"paper":{"title":"Super-linear scaling of offsprings at criticality in branching processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"physics.data-an","authors_text":"A. Saichev, D. Sornette","submitted_at":"2013-05-03T12:24:15Z","abstract_excerpt":"For any branching process, we demonstrate that the typical total number $r_{\\rm mp}(\\nu \\tau)$ of events triggered over all generations within any sufficiently large time window $\\tau$ exhibits, at criticality, a super-linear dependence $r_{\\rm mp}(\\nu \\tau) \\sim (\\nu \\tau)^\\gamma$ (with $\\gamma >1$) on the total number $\\nu \\tau$ of the immigrants arriving at the Poisson rate $\\nu$. In branching processes in which immigrants (or sources) are characterized by fertilities distributed according to an asymptotic power law tail with tail exponent $1 < \\gamma \\leqslant 2$, the exponent of the super"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0684","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"}