  In this paper, we present a fluctuation analysis of a type of parabolic
equations with large, highly oscillatory, random potentials around the
homogenization limit. With a Feynman-Kac representation, the Kipnis-Varadhan's
method, and a quantitative martingale central limit theorem, we derive the
asymptotic distribution of the rescaled error between heterogeneous and
homogenized solutions under different assumptions in dimension $d\geq 3$. The
results depend highly on whether a stationary corrector exits.
