In the spirit of the large-scale elliptic regularity for random elliptic operators obtained by homogenization theory in the recent years, it is natural to investigate what kind of dispersion properties can be proved for classical waves in disordered media.
As localized eigenvalues may appear in general for heterogeneous operators (in the whole space) even in the lower spectrum, dispersive estimates cannot hold in their standard form: eigenvalues lead to time-periodic solutions that do not satisfy any time decay. In this talk I will introduce a weaker form of dispersive estimates that hold for the acoustic operator in disordered media. As an application, I will show how they imply lower bounds on the supports of eigenfunctions (should they exist). This is a joint work with Mitia Duerinckx (ULB).
