| Abstract: | 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 |
