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On Eigenvalue Spacings for the 1-D Anderson Model with Singular Site Distribution

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Geometric Aspects of Functional Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2116))

Abstract

We study eigenvalue spacings and local eigenvalue statistics for 1D lattice Schrödinger operators with Hölder regular potential, obtaining a version of Minami’s inequality and Poisson statistics for the local eigenvalue spacings. The main additional new input are regularity properties of the Furstenberg measures and the density of states obtained in some of the author’s earlier work.

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References

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Acknowledgements

The author is grateful to an anonymous referee and A. Klein for comments and to the UC Berkeley mathematics department for their hospitality. This work was partially supported by NSF grant DMS-1301619.

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Authors and Affiliations

  1. Institute for Advanced Study, Princeton, NJ, 08540, USA

    Jean Bourgain

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  1. Jean Bourgain
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Correspondence to Jean Bourgain .

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Editors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

    Bo'az Klartag

  2. Technion - Israel Institute of Technology, Haifa, Israel

    Emanuel Milman

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Bourgain, J. (2014). On Eigenvalue Spacings for the 1-D Anderson Model with Singular Site Distribution. In: Klartag, B., Milman, E. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2116. Springer, Cham. https://doi.org/10.1007/978-3-319-09477-9_6

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