  An inequality of K. Marton shows that the joint distribution of a Markov
chain with uniformly contracting transition kernels exhibits concentration. We
prove an analogous inequality for broadcast models on finite trees. We use this
inequality to develop a condition for the sequence of depth-$k$ marginals of a
broadcast model on a rooted infinite tree to form a normal L\'{e}vy family in
terms of the Lipschitz constants of the transition kernels and the growth rate
of the tree.
