{"paper":{"title":"A recursive distribution equation for the stable tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Franz Rembart, Matthias Winkel, Nicholas Chee","submitted_at":"2018-12-20T15:27:10Z","abstract_excerpt":"We provide a new characterisation of Duquesne and Le Gall's $\\alpha$-stable tree, $\\alpha\\in(1,2]$, as the solution of a recursive distribution equation (RDE) of the form $\\mathcal{T}\\overset{d}{=}g(\\xi,\\mathcal{T}_i, i\\geq0)$, where $g$ is a concatenation operator, $\\xi = (\\xi_i, i\\geq 0)$ a sequence of scaling factors, $\\mathcal{T}_i$, $i \\geq 0$, and $\\mathcal{T}$ are i.i.d. trees independent of $\\xi$. This generalises a version of the well-known characterisation of the Brownian Continuum Random Tree due to Aldous, Albenque and Goldschmidt. By relating to previous results on a rather differ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08636","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"}