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In this paper we derive quantitative estimates in the context of stochastichomogenization for integral functionals defined on finite partitions, where therandom surface integrand is assumed to be stationary. Requiring the integrandto satisfy in addition a multiscale functional inequality, we controlquantitatively the fluctuations of the asymptotic cell formulas defining thehomogenized surface integrand. As a byproduct we obtain a simplified cellformula where we replace cubes by almost flat hyperrectangles.

Fluctuation estimates for the multi-cell formula in stochastic homogenization of partitions