On localization in the continuous Anderson-Bernoulli model in higher dimension
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Publication:2487928
DOI10.1007/s00222-004-0435-7zbMath1084.82005OpenAlexW1967068708MaRDI QIDQ2487928
Carlos E. Kenig, Jean Bourgain
Publication date: 17 August 2005
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00222-004-0435-7
Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Random linear operators (47B80)
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Cites Work
- Unnamed Item
- Unnamed Item
- A new proof of localization in the Anderson tight binding model
- Some harmonic analysis questions suggested by Anderson-Bernoulli models. Appendix by T.H.Wolff
- Localization for some continuous, random Hamiltonians in \(d\)-dimensions
- Localization of classical waves. I: Acoustic waves
- Anderson localization for Bernoulli and other singular potentials
- Localization for random Schrödinger operators on \(L^ 2 (\mathbb{R}^ d)\): a semiclassical model
- Localization for one-dimensional, continuum, Bernoulli-Anderson models.
- Localization for some continuous random Schrödinger operators
- Operators with singular continuous spectrum. IV: Hausdorff dimensions, rank one perturbations, and localization
- Uniqueness theorems for second order elliptic differential equations
- ON THE POSSIBLE RATE OF DECAY AT INFINITY OF SOLUTIONS OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS
- Bootstrap multiscale analysis and localization in random media