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A note on disagreement percolation
Author(s) -
Häggström Olle
Publication year - 2001
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.1008
Subject(s) - counterexample , markov chain , uniqueness , percolation (cognitive psychology) , independence (probability theory) , mathematics , statistical physics , gibbs measure , coupling (piping) , path (computing) , discrete mathematics , mathematical economics , pure mathematics , statistics , computer science , physics , mathematical analysis , psychology , engineering , neuroscience , programming language , mechanical engineering
We construct a coupling of two distinct Gibbs measures for Markov random fields with the same specifications, such that the existence of an infinite path of disagreements between the two configurations has probability 0. This shows that the independence assumption in the disagreement percolation method for proving Gibbsian uniqueness cannot be dropped without being replaced by other conditions. A similar counterexample is given for couplings of Markov chains. © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 18, 267–278, 2001