Year: 2026
Type: article
Abstract: In the broadcasting problem on trees, a $$\{-1,1\}$$ { - 1 , 1 } -message originating in an unknown node is passed along the tree with a certain error probability q . The goal is to estimate the original message without knowing the order in which the nodes were informed. We show a connection to random walks with memory effects and use this to develop a novel approach to analyze the majority estimator on random recursive trees. With this powerful approach, and a Pólya urn representation, we study the entire group of very simple increasing trees as well as shape exchangeable trees together. This also extends Addario-Berry et al. [8] who investigated this estimator for uniform and linear preferential attachment random recursive trees.
Authors: Ernst Althaus, Lisa Hartung, Rebecca Steiner
Institution: Johannes Gutenberg University Mainz
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W4396815006