Concentration of Broadcast Models on Trees

Christopher Shriver

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arXiv · 1908.08121

Concentration of Broadcast Models on Trees

Christopher Shriver

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Abstract

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.

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Christopher Shriver. 2019-08-21. Concentration of Broadcast Models on Trees. https://arxiv.org/abs/1908.08121

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