Broadcasting on random recursive trees

We study the broadcasting problem when underlying tree is a random recursive tree. The root of has bit value assigned. Every other vertex same as its parent with probability 1?q and opposite q, where q?[0,1]. consists in estimating upon observing unlabeled tree, together associated every vertex. In more difficult version problem, observed but only values leaves are observed. When uniform both variants we characterize q for which optimal reconstruction method error bounded away from 1/2. also show that by constant times q. Two simple rules analyzed detail. One them majority vote, centroid Most results extended to linear preferential attachment trees well.