In the broadcasting problem on trees, a $\{0,1\}$-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. A variation of the problem is considering this broadcasting process on a randomly growing tree, which Addario-Berry et al. have investigated for uniform and linear preferential attachment recursive trees. We extend their studies of the majority estimator to the entire group of very simple increasing trees as well as shape exchangeable trees using the connection to inhomogeneous random walks and other stochastic processes with memory effects such as P\'olya Urns.

翻译：在树的广播问题中，一个源自未知节点的{0,1}消息以一定错误概率q沿树传递。目标是在不知道节点接收顺序的情况下估计原始消息。该问题的变体考虑在随机增长树上的广播过程，Addario-Berry等人已针对均匀和线性优先连接递归树对此进行了研究。我们利用与不均匀随机游走及其他具有记忆效应的随机过程（如波利亚罐模型）的联系，将多数估计器的研究扩展至整个极简递增树类以及形状可交换树。