Noise sensitivity for Voronoi Percolation

Noise sensitivity is a concept that measures if the outcome of a Boolean function can be predicted when one is given its value for a perturbation of the input. A sequence of functions is noise sensitive when this is asymptotically not possible. A non-trivial example of a sequence that is noise sensitive is the crossing functions in critical two-dimensional Bernoulli percolation. In this setting, noise sensitivity can be understood via the study of randomized algorithms. Together with a discretization argument, these techniques can be extended to the continuum setting. In this talk, we prove noise sensitivity for critical Voronoi percolation in dimension two, and derive some consequences of it. Based on a joint work with D. Ahlberg.