Hugo Vanneuville (Lyon): Dynamical Voronoi percolation

Consider a Poisson point process in the plane, construct its Voronoi tiling, and colour each tile in black with probability 1/2 and in white with probability 1/2. This defines a critical Voronoi percolation configuration. We prove that, if we let each point move according to a long range stable Lévy process, then there exist atypical (random) times with an unbounded monochromatic component. To this purpose, we study a continuous spectral object - the annealed spectral sample - which is a continuous analogue of the spectral sample studied by Garban, Pete and Schramm.