  In this paper, we analyze the random fluctuations in a one dimensional
stochastic homogenization problem and prove a central limit result, i.e., the
first order fluctuations can be described by a Gaussian process that solves an
SPDE with additive spatial white noise. Using a probabilistic approach, we
obtain a precise error decomposition up to the first order, which helps to
decompose the limiting Gaussian process, with one of the components
corresponding to the corrector obtained by a formal two scale expansion.
