Localisation of the continuous Anderson Hamiltonian in 1d – Cyril Labbé

Cyril Labbé
CEREMADE, Université Paris-Dauphine
https://www.ceremade.dauphine.fr/~labbe/

Date(s) : 05/05/2017   iCal
11 h 00 min - 12 h 00 min

We consider the Anderson Hamiltonian with a white noise potential on a segment of length L and endowed with Dirichlet boundary conditions. We show that, as L goes to infinity, the (appropriately rescaled and shifted) eigenvalues converge to a Poisson point process on R with an explicit intensity, and that the eigenfunctions converge to Dirac masses located at iid uniform points. Furthermore, we show that the shape of every eigenfunction near 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).

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