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arXiv · 1603.08423

Correlation bound for distant parts of factor of IID processes

Ágnes Backhausz·Balázs Gerencsér·Viktor Harangi·Máté Vizer
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Abstract

We study factor of i.i.d. processes on the $d$-regular tree for $d \geq 3$. We show that if such a process is restricted to two distant connected subgraphs of the tree, then the two parts are basically uncorrelated. More precisely, any functions of the two parts have correlation at most $k(d-1) / (\sqrt{d-1})^k$, where $k$ denotes the distance of the subgraphs. This result can be considered as a quantitative version of the fact that factor of i.i.d. processes have trivial 1-ended tails.

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Ágnes Backhausz, Balázs Gerencsér, Viktor Harangi, Máté Vizer. 2016-03-28. Correlation bound for distant parts of factor of IID processes. https://arxiv.org/abs/1603.08423

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