Abstract
We prove localization at high disorder or low energy for lattice Schrödinger operators with random potentials whose values at different lattice sites are correlated over large distances. The class of admissible random potentials for our multiscale analysis includes potentials with a stationary Gaussian distribution whose covariance functionC(x,y) decays as |x−y|−θ, where θ>0 can be arbitrarily small, and potentials whose probability distribution is a completely analytical Gibbs measure. The result for Gaussian potentials depends on a multivariable form of Nelson's best possible hypercontractive estimate.
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Communicated by T. Spencer
Partially supported by the NSF under grant PHY8515288
Partially supported by the NSF under grant DMS8905627
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von Dreifus, H., Klein, A. Localization for random Schrödinger operators with correlated potentials. Commun.Math. Phys. 140, 133–147 (1991). https://doi.org/10.1007/BF02099294
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DOI: https://doi.org/10.1007/BF02099294