Reconstruction on Trees and Low-Degree Polynomials. (arXiv:2109.06915v2 [math.PR] UPDATED)

The study of Markov processes and broadcasting on trees has deep connections
to a variety of areas including statistical physics, graphical models,
phylogenetic reconstruction, MCMC algorithms, and community detection in random
graphs. Notably, the celebrated Belief Propagation (BP) algorithm achieves
optimal performance for the reconstruction problem of predicting the value of
the Markov process at the root of the tree from its values at the leaves.

Recently, the analysis of low-degree polynomials has emerged as a valuable
tool for predicting …

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