02-471 David Damanik, Robert Sims, G\"unter Stolz

Localization for discrete one dimensional random word models (454K, Postscript) Nov 20, 02

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Abstract. We consider discrete one-dimensional Schr\"odinger operators whose potentials are obtained by randomly concatenating words from an underlying word space according to some probability measure. 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.

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