Consider the evolution of sets by forced mean curvature flow through a field of random obstacles. The effective large scale behaviour is expected to be a first order motion. However, previous results heavily relied on the assumption that there is a global minimum speed of expansion and hence on the absence of any actual obstacles.
We obtain a quantitative homogenization result even with actual obstacles, potentially allowing the interface to get stuck locally, eventually leading to enclosures behind a main front. So far in this regime not even a qualitative stochastic homogenization result had been available. The existence of a global minimum speed is replaced with a probabilistic assumption. We assume that on large scales with high probability ‘fat’ sets can be approximated from within by sets which are increasing with respect to the evolution and expand at an ‘effective’ minimum speed - that is, we ignore smaller holes left behind. This assumption is satisfied for example if the obstacles are distributed according to a Poisson point process with low enough intensity. The talk is based on joint work with Julian Fischer (Institute of Science and Technology Austria).