2019/04/28 by Andrei Alpeev, Alpeev, Andrei
Computer Science · Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cs.IT #math.DS #math.IT #math.PR
paper · pdf · doi:10.48550/arxiv.1904.12352
14 pages
arxiv created 2019/04/28 · arxiv updated 2019/04/30
In a recent paper by A. Backhausz, B. Gerencsér and V. Harangi, it was shown that factors of independent identically distributed random processes (IID) on trees obey certain geometry-driven inequalities. In particular, the mutual information shared between two vertices decays exponentially, and there is an explicit bound for this decay. In this note we show that all of these inequalities could be verbatim translated to the setting of factors of processes driven by unique Gibbs measures. As a consequence, we show that correlations decay exponentially for unique Gibbs measures on trees.