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

Springer Science and Business Media LLC - Tập 161 - Trang 389-426 - 2005
Jean Bourgain1, Carlos E. Kenig2
1School of Mathematics, Institute for Advanced Study, Princeton, USA
2Department of Mathematics, University of Chicago, chicago, (USA)

Tài liệu tham khảo

Bollobas, B.: Combinatorics. Cambridge UP 1986 Bourgain, J.: On localization for lattice Schrödinger operators involving Bernoulli variables. Lect. Notes Math., vol. 1850, pp. 77–100. Springer 2004 Carmona, R., Klein, A., Martinelli, F.: Anderson localization for Bernoulli and other singular potentials. Comm. Math. Phys. 108, 41–66 (1987) Combes, J.M., Hislop, P.D.: Localization for some continuous, random Hamiltonians in d-dimensions. J. Funct. Anal. 124, 149–180 (1994) von Dreifus, H., Klein, A.: A new proof of localization in the Anderson tight binding model. Comm. Math. Phys. 124, 285–299 (1989) Damanik, D., Sims, R., Stolz, G.: Localization for one dimensional, continuum, Bernoulli-Anderson Models. Duke Math. J. 114, 59–100 (2002) Escauriaza, L., Vessella, S.: Optimal three-cylinder inequalities for solutions to parabolic equations with Lipschitz leading coefficients. Comtemp. Math. 333, 79–87 (2003) Figotin, A., Klein, A.: Localization of classical waves I: Acoustic waves. Comm. Math. Phys. 180, 439–482 (1996) Germinet, F., Klein, A.: Bootstrap Multiscale Analysis and Localization in Random Media. Comm. Math. Phys. 222, 415–448 (2001) Hörmander, L.: Uniqueness theorems for second order elliptic differential equations. Comm. Partial Differential Equations 8, 21–64 (1983) 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 Klopp, F.: Localization for some continuous random Schrödinger operators. Comm. Math. Phys. 167, 553–569 (1995) Klopp, F.: Localisation pour des opérateurs de Schrödinger aléatoires dans L2(Rd); un modèle semi-classique. Ann. Inst. Fourier 45, 265–316 (1995) 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) 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) Shubin, C., Vakilian, T., Wolff, T.: Some harmonic Analysis questions suggested by Anderson/Bernoulli models. Geom. Funct. Anal. 8, 932–964 (1988)