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In this paper, we analyze the random fluctuations in a one dimensionalstochastic homogenization problem and prove a central limit result, i.e., thefirst order fluctuations can be described by a Gaussian process that solves anSPDE with additive spatial white noise. Using a probabilistic approach, weobtain a precise error decomposition up to the first order, which helps todecompose the limiting Gaussian process, with one of the componentscorresponding to the corrector obtained by a formal two scale expansion.

A central limit theorem for fluctuations in one dimensional stochastic homogenization