2026-07-21T19:58:22Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:26275 2026-07-13T15:02:35Z ddc:004 open_access

Scaling Limits of Multitype Bienaymé Trees Addario-Berry, Louigi Beltran, Philipp Stufler, Benedikt Thévenin, Paul branching processes multitype trees scaling limit We first consider irreducible critical multitype Bienaymé trees and extend the results to the case, when they possess a critical irreducible component with attached subcritical components. We study these trees under two distinct conditioning frameworks: first, conditioning on the value of a linear combination of the numbers of vertices of given types; and second, conditioning on the precise number of vertices belonging to a selected subset of types. We prove that, under a finite exponential moment condition, the scaling limit as the tree size tends to infinity is given by the Brownian Continuum Random Tree. Additionally, we establish strong non-asymptotic tail bounds for the height of such trees. Our main tools include a flattening operation applied to multitype trees and sharp estimates regarding the structure of monotype trees with a given sequence of degrees. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Louigi Addario-Berry and Philipp Beltran and Benedikt Stufler and Paul Thévenin 2026 Is Part Of LIPIcs, Volume 381, 37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.AofA.2026.4 urn:nbn:de:0030-drops-262750 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2026.4 eng https://creativecommons.org/licenses/by/4.0/legalcode