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Correlation Bounds for Distant Parts of Factor of IID Processes

  • ÁGNES BACKHAUSZ (a1) (a2), BALÁZS GERENCSÉR (a1) (a2), VIKTOR HARANGI (a2) and MÁTÉ VIZER (a2)

Abstract

We study factor of i.i.d. processes on the d-regular tree for d ≥ 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 between 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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Keywords

Correlation Bounds for Distant Parts of Factor of IID Processes

  • ÁGNES BACKHAUSZ (a1) (a2), BALÁZS GERENCSÉR (a1) (a2), VIKTOR HARANGI (a2) and MÁTÉ VIZER (a2)

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