Skip to main content

On localization in the continuous Anderson-Bernoulli model in higher dimension

This is a preview of subscription content, access via your institution.

References

  1. Bollobas, B.: Combinatorics. Cambridge UP 1986

  2. Bourgain, J.: On localization for lattice Schrödinger operators involving Bernoulli variables. Lect. Notes Math., vol. 1850, pp. 77–100. Springer 2004

  3. Carmona, R., Klein, A., Martinelli, F.: Anderson localization for Bernoulli and other singular potentials. Comm. Math. Phys. 108, 41–66 (1987)

    Article  Google Scholar 

  4. Combes, J.M., Hislop, P.D.: Localization for some continuous, random Hamiltonians in d-dimensions. J. Funct. Anal. 124, 149–180 (1994)

    Article  Google Scholar 

  5. von Dreifus, H., Klein, A.: A new proof of localization in the Anderson tight binding model. Comm. Math. Phys. 124, 285–299 (1989)

    Article  Google Scholar 

  6. Damanik, D., Sims, R., Stolz, G.: Localization for one dimensional, continuum, Bernoulli-Anderson Models. Duke Math. J. 114, 59–100 (2002)

    Article  Google Scholar 

  7. Escauriaza, L., Vessella, S.: Optimal three-cylinder inequalities for solutions to parabolic equations with Lipschitz leading coefficients. Comtemp. Math. 333, 79–87 (2003)

    Google Scholar 

  8. Figotin, A., Klein, A.: Localization of classical waves I: Acoustic waves. Comm. Math. Phys. 180, 439–482 (1996)

    Google Scholar 

  9. Germinet, F., Klein, A.: Bootstrap Multiscale Analysis and Localization in Random Media. Comm. Math. Phys. 222, 415–448 (2001)

    Article  Google Scholar 

  10. Hörmander, L.: Uniqueness theorems for second order elliptic differential equations. Comm. Partial Differential Equations 8, 21–64 (1983)

    Google Scholar 

  11. Klein, A.: Multiscale Analysis and Localization. Lectures given at Random Schrödinger operators: methods, results, and perspectives. To appear in États de la recherche, Université Paris 13, June 2002

  12. Klopp, F.: Localization for some continuous random Schrödinger operators. Comm. Math. Phys. 167, 553–569 (1995)

    Google Scholar 

  13. Klopp, F.: Localisation pour des opérateurs de Schrödinger aléatoires dans L2(Rd); un modèle semi-classique. Ann. Inst. Fourier 45, 265–316 (1995)

    Google Scholar 

  14. Meshkov, V.: On the possible role of decay at infinity of solutions of second order partial differential equations. Math. USSR Sbornik 72, 343–351 (1992)

    Google Scholar 

  15. del Rio, R., Jitomirskaya, S., Last, Y., Simon, B.: Operators with singular continuous spectrum, IV. Hausdorff dimensions, rank one perturbations, and localization. J. Anal. Math. 69, 153–200 (1996)

    Google Scholar 

  16. Shubin, C., Vakilian, T., Wolff, T.: Some harmonic Analysis questions suggested by Anderson/Bernoulli models. Geom. Funct. Anal. 8, 932–964 (1988)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jean Bourgain.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bourgain, J., Kenig, C. On localization in the continuous Anderson-Bernoulli model in higher dimension. Invent. math. 161, 389–426 (2005). https://doi.org/10.1007/s00222-004-0435-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00222-004-0435-7

Keywords

  • High Dimension