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This paper is concerned with the behavior of the homogenized coefficientsassociated with some random stationary ergodic medium under a Bernoulliperturbation. Introducing a new family of energy estimates that combineprobability and physical spaces, we prove the analyticity of the perturbedhomogenized coefficients with respect to the Bernoulli parameter. Our approachholds under the minimal assumptions of stationarity and ergodicity, both in thescalar and vector cases, and gives analytical formulas for each derivative thatessentially coincide with the so-called cluster expansion used by physicists.In particular, the first term yields the celebrated (electric and elastic)Clausius-Mossotti formulas for isotropic spherical random inclusions in anisotropic reference medium. This work constitutes the first general proof ofthese formulas in the case of random inclusions.

Analyticity of homogenized coefficients under Bernoulli perturbations and the Clausius-Mossotti formulas