Malo Hillairet: Noise Sensitivity in First-Passage Percolation


Abstract

First-Passage Percolation is a spatial growth model where the objects of interest are called travel times. Travel times are defined as geodesic lengths in a random environment. A surprising and counter-intuitive phenomenon that could arise in First-Passage Percolation is called noise sensitivity. It is the property that small noise on the environment leads to drastic perturbations of travel times. We generalize a known noise sensitivity result which initially does not apply to our context, the BKS theorem, in order to deduce noise sensitivity properties in First-Passage Percolation.