Abstract
Complete localization is shown to hold for the d-dimensional Anderson model with uniformly distributed random potentials provided the disorder strength \({\lambda > \lambda_{And}}\) where \({\lambda_{\rm And}}\) satisfies \({\lambda_{\rm And}}=\mu_d e \ln \lambda_{\rm And}\) with \({\mu_d}\) the self-avoiding walk connective constant for the lattice \({\mathbb{Z}^d}\) . Notably, \({\lambda_{\rm And}}\) is precisely the large disorder threshold proposed by Anderson in 1958.
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Supported by NSF CAREER Award DMS-08446325.
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Schenker, J. How Large is Large? Estimating the Critical Disorder for the Anderson Model. Lett Math Phys 105, 1–9 (2015). https://doi.org/10.1007/s11005-014-0729-7
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DOI: https://doi.org/10.1007/s11005-014-0729-7