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

created by ruf on 18 Mar 2021
modified on 27 Apr 2021

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Preprint

Inserted: 18 mar 2021
Last Updated: 27 apr 2021

Year: 2021

Abstract:

In this paper we derive quantitative estimates in the context of stochastic homogenization for integral functionals defined on finite partitions, where the random surface integrand is assumed to be stationary. Requiring the integrand to satisfy in addition a multiscale functional inequality, we control quantitatively the fluctuations of the asymptotic cell formulas defining the homogenized surface integrand. As a byproduct we obtain a simplified cell formula where we replace cubes by almost flat hyperrectangles.