In this talk, we will be interested in the semclassical eigenfunctions of the Laplace-Beltrami operator on a compact manifold, or of a Schrödinger operator with a confining potential in the Euclidean space.We will consider the L∞ norms of these semiclassical eigenfunctions, which reflect their localisation or delocalisation properties. After recalling the existing results and conjectures, we will show how these results can be improved by adding small random perturbations to the operators we consider. These are joint works with Martin Vogel and Alb Garcia-Ruiz.
