TY - JOUR
T1 - Localization for discrete one-dimensional random word models
AU - Damanik, David
AU - Sims, Roberts
AU - Stolz, Günter
N1 - 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 Université 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: [email protected] (D. Damanik), [email protected] (R. Sims), [email protected] (G. Stolz).
PY - 2004/3/15
Y1 - 2004/3/15
N2 - We consider Schrödinger 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.
AB - We consider Schrödinger 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.
KW - Anderson model
KW - Localization
KW - Random operators
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U2 - 10.1016/j.jfa.2003.07.011
DO - 10.1016/j.jfa.2003.07.011
M3 - Article
AN - SCOPUS:1542511261
SN - 0022-1236
VL - 208
SP - 423
EP - 445
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 2
ER -