*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.