Fluctuation estimates for the blow-up formula in stochastic homogenisation of partitions

This talk is concerned with quantitative estimates in the context of stochastic homogenisation of random integral functionals defined on finite partitions. Assuming the integrand to be stationary, the techniques to determine the homogenised limiting functional in terms of Γ-convergence are by now quite well established. Here the homogenised limiting integrand is obtained via a blow-up formula by solving minmisation problems on larger and larger cubes. In this talk we show that the cubes in these minimisation problems can actually be replaced by almost flat hyperrectangles and we explain how to control quantitatively the fluctuation of the corresponding blow-up formulas.

This is joint work with Matthias Ruf (EPFL).