INTERACTING RANDOM-WALK IN A DYNAMICAL RANDOM ENVIRONMENT .2. ENVIRONMENT FROM THE POINT-OF-VIEW OF THE PARTICLE

We consider, as in I, a random walk X(t) is-an-element-of Z(nu), t is- an-element-of Z+ and a dynamical random field xi(t) (x), x is-an-eleme nt-of Z(nu) in mutual interaction with each other. The model is a pert urbation of un unperturbed model in which walk and field evolve indepe ndently. Here we consider the environment process in a frame of refere nce that moves with the walk, i.e., the ''field from the point of view of the particle'' eta(t) (.) = xi(t) (X(t) + .). We prove that its di stribution tends, as t --> infinity, to a limiting distribution mu, wh ich is absolutely continuous with respect to the unperturbed equilibri um distribution. We also prove that, for nu less-than-or-equal-to 3, t he time correlations of the field eta(t) decay as const [GRAPHICS]