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Correlation Bounds for Distant Parts of Factor of IID Processes

Published online by Cambridge University Press:  01 August 2017

ÁGNES BACKHAUSZ ,
BALÁZS GERENCSÉR ,
VIKTOR HARANGI  and
MÁTÉ VIZER
ÁGNES BACKHAUSZ
Affiliation:
Department of Probability and Statistics, Eötvös Loránd University, Pázmány Péter sétány 1/c, H-1117 Budapest, Hungary (e-mail: agnes@cs.elte.hu) MTA Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, H-1053 Budapest, Hungary (e-mail: gerencser.balazs@renyi.mta.hu, harangi@renyi.hu, vizermate@gmail.com)
BALÁZS GERENCSÉR
Affiliation:
Department of Probability and Statistics, Eötvös Loránd University, Pázmány Péter sétány 1/c, H-1117 Budapest, Hungary (e-mail: agnes@cs.elte.hu) MTA Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, H-1053 Budapest, Hungary (e-mail: gerencser.balazs@renyi.mta.hu, harangi@renyi.hu, vizermate@gmail.com)
VIKTOR HARANGI
Affiliation:
MTA Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, H-1053 Budapest, Hungary (e-mail: gerencser.balazs@renyi.mta.hu, harangi@renyi.hu, vizermate@gmail.com)
MÁTÉ VIZER
Affiliation:
MTA Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, H-1053 Budapest, Hungary (e-mail: gerencser.balazs@renyi.mta.hu, harangi@renyi.hu, vizermate@gmail.com)
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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.

Keywords

Primary 60K35Secondary 37A50

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 27 , Issue 1 , January 2018 , pp. 1 - 20
Copyright
Copyright © Cambridge University Press 2017 

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