A Random Walk Approach to Broadcasting on Random Recursive Trees

TL;DR

This paper introduces a novel random walk-based method to analyze broadcasting on random recursive trees, providing insights into the majority estimator's performance across various tree models.

Contribution

It develops a new approach connecting random walks with memory effects to analyze broadcasting, extending prior work to broader classes of trees.

Findings

Analyzed majority estimator on various random recursive trees

Extended results to shape exchangeable trees

Provided new insights into broadcasting accuracy

Abstract

In the broadcasting problem on trees, a $\{-1,1\}$-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 analyse the majority estimator on random recursive trees. With this powerful approach, we study the entire group of very simple increasing trees as well as shape exchangeable trees together. This also extends Addario-Berry et al. (2022) who investigated this estimator for uniform and linear preferential attachment random recursive trees.