KTH/SU Mathematics Colloquium
08-05-14
Nalini Anantharaman, Ecole Polytechnique
Entropy and localization of eigenfunctions
On a compact negatively curved manifold, we study the asymptotic behaviour
of the eigenfunctions $(\phi_n)$ of the laplacian, when the eigenvalue
$\lambda_n$ goes to infinity. The Quantum Unique Ergodicity conjecture
says that the probability measures $|\phi_n(x)|^2dx$ should converge
weakly to the riemannian volume (the uniform measure). We prove a result
going in this direction, saying that the `dynamical' entropy of these
measures is asymptotically positive.
The colloquium talk will be an introduction to the subject. In a
follow-up talk in the DNA-seminar more details about the proof and
recent developments will given.