  We study the motion of independent particles in a dynamical random
environment on the integer lattice. The environment has a product distribution.
For the multidimensional case, we characterize the class of spatially ergodic
invariant measures. These invariant distributions are mixtures of inhomogeneous
Poisson product measures that depend on the past of the environment. We also
investigate the correlations in this measure. For dimensions one and two, we
prove convergence to equilibrium from spatially ergodic initial distributions.
In the one-dimensional situation we study fluctuations of the net current seen
by an observer traveling at a deterministic speed. When this current is
centered by its quenched mean its limit distributions are the same as for
classical independent particles.
