Geodesic
A comprehensive proof of localization for continuous Anderson models with singular random potentials
Journal of the European Mathematical Society, Tome 15 (2013) no. 1, pp. 53-143

Voir la notice de l'article provenant de la source EMS Press

We study continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We prove the existence of a strong form of localization at the bottom of the spectrum, which includes Anderson localization (pure point spectrum with exponentially decaying eigenfunctions) with finite multiplicity of eigenvalues, dynamical localization (no spreading of wave packets under the time evolution), decay of eigenfunctions correlations, and decay of the Fermi projections. We also prove log-Hölder continuity of the integrated density of states at the bottom of the spectrum.
DOI : 10.4171/jems/356
Classification : 82-XX, 47-XX, 60-XX, 81-XX
Keywords: Anderson localization, dynamical localization, random Schrödinger operator, continuous Anderson model, integrated density of states 
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     title = {A comprehensive proof of localization for continuous {Anderson} models with singular random potentials},
     journal = {Journal of the European Mathematical Society},
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François Germinet; Abel Klein. A comprehensive proof of localization for continuous Anderson models with singular random potentials. Journal of the European Mathematical Society, Tome 15 (2013) no. 1, pp. 53-143. doi: 10.4171/jems/356

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