Rotationally invariant first passage percolation: Chaos

Last May I spoke about a series of multi-scale arguments to establish scaling relations for rotationally invariant first passage percolation in the plane. In this talk I will discuss how these methods can be used to establish the chaotic nature of the optimal path, that is, after a small resampling, the new optimal path has vanishing overlap with the original. By applying this in a multiscale scheme we get new upper bounds on the variance of the passage times.