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Probabilidade e Combinatória

Localization of the continuous Anderson hamiltonian in 1d
Cyril Labbé

Université Paris Dauphine
Sexta-feira, 22 de junho de 2018, 13:30
Sala 224

We consider the operator obtained by perturbing the Laplacian with a white noise on a segment of size L. This operator arises as scaling limit of simple random matrix models, and plays an important role in the study of the parabolic Anderson model. We show that, as L goes to infinity, the eigenvalues converge to a Poisson point process on R with an explicit intensity, and the eigenfunctions converge to Dirac masses located at iid uniform points. Furthermore, we show that the asymptotic shape of each eigenfunction around its maximum is given by an explicit, deterministic function which does not depend on the corresponding eigenvalue. This is a joint work with Laure Dumaz (Paris-Dauphine).