@article{6be0af3c34cf4f76b2bb43a601fb4ff9,
title = "Localization for discrete one-dimensional random word models",
abstract = "We consider Schr{\"o}dinger operators in ℓ2(ℤ) whose potentials are obtained by randomly concatenating words from an underlying set W according to some probability measure ν on W. Our assumptions allow us to consider models with local correlations, such as the random dimer model or, more generally, random polymer models, We prove spectral localization and, away from a finite set of exceptional energies, dynamical localization for such models. These results are obtained by employing scattering theoretic methods together with Furstenberg's theorem to verify the necessary input to perform a multiscale analysis.",
keywords = "Anderson model, Localization, Random operators",
author = "David Damanik and Roberts Sims and G{\"u}nter Stolz",
note = "Funding Information: The authors are grateful for an invitation to the Mittag-Leffler Institute in Fall 2002, where this work was completed. G.S. also acknowledges the hospitality of Universit{\'e} Paris 7 and financial support of CNRS (France). We would like to thank Michael Levitin, Elliot Lieb, Eric Rains, and Shannon Starr for useful discussions and comments. Funding Information: $D.D. was supported in part by NSF Grant DMS-0227289, G.S. by NSF Grant DMS–0070343. R.S. is supported through an NSF Postdoctoral Fellowship. ·Corresponding author. Fax: +205-943-9025. E-mail addresses: damanik@its.caltech.edu (D. Damanik), rsims@princeton.edu (R. Sims), stolz@math.uab.edu (G. Stolz).",
year = "2004",
month = mar,
day = "15",
doi = "10.1016/j.jfa.2003.07.011",
language = "English (US)",
volume = "208",
pages = "423--445",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "2",
}