Title: Invariant measures for passive tracer dynamics.
Abstract: Passive tracer model describes the diffusion of a particle in a random environment. One of the principal questions in the asymptotic analysis of the particle motion is the existence of an invariant measure for the process describing the environment as viewed from the moving particle, the so called environment process. There are only few special cases when this invariant measure is explicitly known. We give sufficient conditions for the existence of an invariant measure that is absolutely continuous w.r.t. the probability measure describing randomness of the environment. These conditions usually take form of a sufficiently strong mixing assumption about the temporal dynamics of the environment, or in the static case, a sufficiently strongly mixing in space and a non-vanishing mean drift that dominates the fluctuations of the environment.