Entropy and the localization of eigenfunctions

Entropy and the localization of eigenfunctions

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Nalini Anantharaman, Ecole Polytechnique
Fine Hall 314

We study the behaviour of the eigenfunctions of the laplacian, on a compact negatively curved manifold, and for large eigenvalues. The Quantum Unique Ergodicity conjecture predicts that the probability measures defined by these eigenfunctions should converge weakly to the Riemannian volume. We prove an entropy lower bound on these probability measures, which shows for instance that it is difficult for them to concentrate on closed geodesics.