  The paper studies homogenization problem for a non-autonomous parabolic
equation with a large random rapidly oscillating potential in the case of one
dimensional spatial variable. We show that if the potential is a statistically
homogeneous rapidly oscillating function of both temporal and spatial variables
then, under proper mixing assumptions, the limit equation is deterministic and
the convergence in probability holds. To the contrary, for the potential having
a microstructure only in one of these variables, the limit problem is
stochastic and we only prove the convergence in law.
