| Abstract: |
| In the present talk, we will present a novel approach to study the large-scale fluctuations of a class of stationary quasi-linear SPDEs at super-critical dimensions. In particular, we show that this class of SPDEs has Gaussian fluctuations and that the limit is given by a linear additive Stochastic Heat equation with renormalised coefficients. Our approach is based on a suitable two-scale expansion for the generator of our dynamics and extends classical stochastic homogeneization to the infinite-dimensional setting. Byproducts of our methods are that we obtain quantitative rates for the convergence of the microscopic generator to the limiting one and a more transparent characterisation of the macroscopic diffusivity in terms of microscopic observables. Based on joint ongoing work with H. Giles (TU Vienna) and L. Grafner (Warwick). |
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