A VOTER MODEL IN RANDOM ENVIRONMENT

This process (eta(t))(t greater than or equal to 0) has state space {- 1,+1}(Zd), d > 1, where the distribution of the links between each sit e of Zd and its nearest neighbors is the Bernoulli product measure v(p ), 0 < p < 1. The transitions of eta(t)(x), x is an element of Z(d), a re either those of the voter model, or of the anti-voter model, accord ing to the value of its links with its neighbors. We prove that this p rocess is ergodic, using a duality relation similar to the one introdu ced by Matloff for the anti-voter model.