DISTANCE IN TOTAL VARIATION BETWEEN A GIB BS MEASURE AND ITS TRANSLATE

We first prove an inequality for the distance in total variation betwe en a Gibbs measure mu on (R-Zd, B-Rzd) and its transulate eta((b)), wi th b almost equal to zero. Then we prescribe some restrictions for the associated potential which allows, by going to the limit, to obtain a n overestimation of the distance for any b epsilon R-Zd. These results give some conditions for the measures mu and mu((b)) to be equivalent . At last, we give some examples to illustrate the previously establis hed theorems.