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This review is an extended version of my mini course at the Etats de la recherche: Operateurs de Schroedinger aleatoires at the Universite Paris 13 in June 2002, a summer school organized by Frederic Klopp.
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J. Avron, B. Simon: Almost periodic Schrödinger operators. II: The integrated density of states. Duke Math. J. 50, 369-391 (1983)
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J. Fröhlich, T. Spencer: Absence of diffusion in the Anderson tight binding model for large disorder or low energy. Commun. Math. Phys. 88, 151-184 (1983)
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W. Kirsch, F. Martinelli: Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians. Commun. Math. Phys. 89, 27-40 (1983)
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B. Simon: Lifshitz Tails for the Anderson Model. Journal of Statisticl Physics 38, No.1, 65-76 (1985)
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W. Kirsch, B. Simon: Lifshitz tails for periodic plus random potential. J. Stat. Phys. 42, 799 - 808 (1986)
1986
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S. Kotani: Lyapunov exponents and spectra for one-dimensional random Schrödinger operators. Contemp. Math. 50, 277-286 (1986)
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G. A. Mezincescu: Internal Lifschitz singularities of disordered finite-difference Schrödinger operators. Commun. Math. Phys. 103, 167-176 (1986)
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B. Simon, T. Wolff: Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians. Commun. Pure Appl. Math. 39, 75-90 (1986)
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Cited alongside, same era.
T. Spencer: The Schrödinger equation with a random potential. A mathematical review. Critical phenomena, random systems, gauge theories, Proc. Summer Sch. Theor. Phys., Sess. 43, Les Houches/France 1984, Pt. 2, 895-942 (1986)
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L. Erdös: Lifschitz tail in a magnetic field: The nonclassical regime. Probab. Theory Relat. Fields 112, No.3, 321-371 (1998)
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W. Kirsch, P. Stollmann, G. Stolz: Localization for random perturbations of periodic Schrödinger operators. Random Oper. Stoch. Equ. 6, No.3, 241-268 (1998)
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W. Kirsch, P. Stollmann, G. Stolz: Anderson localization for random Schrödinger operators with long range interactions. Commun. Math. Phys. 195, 495-507 (1998)
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A. Klein: Extended states in the Anderson model on the Bethe lattice. Adv. Math. 133, No.1, 163-184 (1998)
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1986
Cited alongside, same era.
D. J. Thouless: Introduction to disordered systems. Critical phenomena, random systems, gauge theories, Proc. Summer Sch. Theor. Phys., Sess. 43, Les Houches/France 1984, Pt. 2, 685-722 (1986)
1986
Cited alongside, same era.
R. Carmona, A. Klein, F. Martinelli: Anderson localization for Bernoulli and other singular potentials. Commun. Math. Phys. 108, 41-66 (1987)
1987
Cited alongside, same era.
H. L. Cycon, R. G. Froese, W. Kirsch, B. Simon: Schrödinger operators, with application to quantum mechanics and global geometry . Texts and Monographs in Physics. Berlin etc.: Springer-Verlag. (1987)
1987
Cited alongside, same era.
H. von Dreifus: On the effects of randomness in ferromagnetic models and Schrödinger operators, NYU PhD thesis (1987)
1987
Cited alongside, same era.
S. Kotani, B. Simon: Localization in general one-dimensional random systems. II. Continuum Schrödinger operators. Commun. Math. Phys. 112, 103-119 (1987)
1987
Cited alongside, same era.
B. Simon: Internal Lifshitz Tails, Journal of Statisticl Physics 46, 911 - 918 (1987)
1987
Cited alongside, same era.
I. M. Lifshits, S. A. Gredeskul, L. A. Pastur: Introduction to the theory of disordered systems . Wiley, New York (1988)
1988
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A. S. Sznitman: Brownian motion, obstacles and random media . Springer Monographs in Mathematics. Berlin: Springer (1998)
1998
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P. Stollmann: Lifshitz asymptotics via linear coupling of disorder. Math. Phys. Anal. Geom. 2, No.3, 279-289 (1999)
1999
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G. Teschl: Jacobi Operators and Completely Integrable Nonlinear Lattices ; AMS 1999
1999
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D. Hundertmark, W. Kirsch: Spectral theory for sparse potentials. CMS Conf. Proc. 28, 213-238 (2000)
2000
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W. Kirsch, M. Krishna, J. Obermeit: Anderson model with decaying randomness: Mobility edge. Math. Z. 235, 421-433 (2000)
2000
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F. Klopp: Precise high energy asymptotics for the integrated density of states of an unbounded random Jacobi matrix. Rev. Math. Phys. 12, No.4, 575-620 (2000)
2000
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P. Stollmann: Wegner estimates and localization for continuum Anderson models with some singular distributions. Arch. Math. 75, 307-311 (2000)
2000
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M. Aizenman, J. H. Schenker, R. M. Friedrich, D. Hundertmark: Finite-volume fractional-moment criteria for Anderson localization. Commun. Math. Phys. 224, No.1, 219-253 (2001)
2001
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H. Bauer: Measure and integration theory , de Gruyter (2001)
2001
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M. Biskup, W. König: Long-time tails in the parabolic Anderson model, Ann. of Prob. 29, No.2, 636–682 (2001)
2001
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D. Damanik, P. Stollmann: Multi-scale analysis implies strong dynamical localization. Geom. Funct. Anal. 11, 11-29 (2001)
2001
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F. Germinet, A. Klein: Bootstrap multiscale analysis and localization in random media. Commun. Math. Phys. 222, 415–448 (2001)
2001
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P. Stollmann: Caught by disorder. Bound states in random media. Progress in Mathematical Physics . 20. Boston: Birkhäuser (2001)
2001
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S. Warzel: On Lifshitz tails in magnetic fields. Dissertation. Universität Erlangen-Nürnberg, Logos (2001)
2001
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J. Bourgain: On random Schrödinger operators on ℤ d \mathbb{Z}^{d} . Discrete Contin. Dyn. Syst. 8, 1–15 (2002)
2002
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D. Damanik, R. Sims, G. Stolz: Localization for one-dimensional, continuum, Bernoulli-Anderson models. Duke Math. J. 114, No.1, 59-100 (2002)
2002
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W. Kirsch: Scattering theory for sparse random potentials. Random Oper. Stoch. Equ. 10, 329-334 (2002)
2002
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F. Klopp: Lifshitz tails for random perturbations of periodic Schrödinger operators. Proc. Indian Acad. Sci., Math. Sci. 112, No.1, 147-162 (2002)
2002
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F. Klopp: Lifshitz tails for random perturbations of periodic Schrödinger operators. Proc. Indian Acad. Sci., Math. Sci. 112, No.1, 147-162 (2002)
2002
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F. Klopp: Weak disorder localization and Lifshitz tails. Commun. Math. Phys. 232, No.1, 125-155 (2002)
2002
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F. Klopp: Weak disorder localization and Lifshitz tails: Continuous Hamiltonians. Ann. Henri Poincaré 3, No.4, 711-737 (2002)
2002
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F. Klopp: Internal Lifshitz tails for Schrödinger operators with random potentials. J. Math. Phys. 43, No.6, 2948-2958 (2002)
2002
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F. Klopp, T. Wolff: Lifshitz tails for 2-dimensional random Schrödinger operators. J. Anal. Math. 88, 63-147 (2002)
2002
Later among the works it cites.
I. Veselic: Localization for random perturbations of periodic Schrödinger operators with regular Floquet eigenvalues Annal. H. Poinc. 3, 389-409 (2002)
2002
Later among the works it cites.
S. Jitomirskaya, H. Schulz-Baldes, G. Stolz: Delocalization in random polymer models. Commun. Math. Phys. 233, 27–48 (2003)
2003
Later among the works it cites.
W. Kirsch, O. Lenoble, L. Pastur: On the Mott formula for the ac conductivity and binary correlators in the strong localization regime of disordered systems. J. Phys. A, Math. Gen. 36, No.49, 12157-12180 (2003)
2003
Later among the works it cites.
W. Kirsch, O. Lenoble, L. Pastur: On the Mott formula for the a.c. conductivity and binary correlators in the strong localization regime of disordered systems, J. Phys. A Math. Gen. 36, 12157–12180 (2003)
2003
Later among the works it cites.
H. Najar: Lifshitz tails for random acoustic operators, J. Math. Phys. 44, 1842–1867 (2003)
2003
Later among the works it cites.
I. Rodnianski, W. Schlag: Classical and quantum scattering for a class of long range random potentials. Int. Math. Res. Not. 5, 243–300 (2003)
2003
Later among the works it cites.
F. Germinet, A. Klein: A characterization of the Anderson metal-insulator transport transition. Duke Math. J. 124, 309-351 (2004)
2004
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I. Veselic: Integrated density and Wegner estimates for random Schrödinger operators. del Rio, Rafael (ed.) et al., Spectral theory of Schrödinger operators. Lecture notes from a workshop, Mexico, December 3-7, 2001. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 340, 97-183 (2004)
2004
Later among the works it cites.
J.-M. Bouclet, F. Germinet, A. Klein, J. Schenker: Linear response theory for magnetic Schrödinger operators in disordered media. J. Funct. Anal. 226, 301–372 (2005)
2005
Later among the works it cites.
J. Bourgain, C. Kenig: On localization in the continuous Anderson-Bernoulli model in higher dimension. Invent. Math. 161, No.2, 389-426 (2005)
2005
Later among the works it cites.
W. Kirsch, S. Warzel: Lifshits tails caused by anisotropic decay: the emergence of a quantum-classical regime. Math. Phys. Anal. Geometry 8, 257–285 (2005)
2005
Later among the works it cites.
B. Metzger: Asymptotische Eigenschaften im Wechselspiel von Diffusion und Wellenausbreitung in zufälligen Medien. Dissertation, TU Chemnitz (2005)
2005
Later among the works it cites.
W. Kirsch, P. Müller: Spectral properties of the Laplacian on bond-percolation graphs. Math. Z. 252, 899–916 (2006)
2006
Later among the works it cites.
W. Kirsch, S. Warzel: Anderson localization and Lifshits tails for random surface potentials. Journal of Functional Analysis 230, 222-250 (2006)
2006
Later among the works it cites.
S. Jitomirskaya: Ergodic Schrödinger operators (on one foot), in: F. Gesztesy, P. Deift, C. Galvez, P. Perry, W. Schlag (Editors): Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon’s 60th Birthday, 613–647 (2007)
2007
Closest in time.
W. Kirsch, B. Metzger: The Integrated Density of States for Random Schrödinger Operators, in: F. Gesztesy, P. Deift, C. Galvez, P. Perry, W. Schlag (Editors): Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon’s 60th Birthday, 649–696 (2007)
2007
Closest in time.