Abstract
Let H be a Jacobi matrix acting on \(\ell ^2 (\mathbb{Z})\) and V ω a random potential of Anderson type. Let H ω = H+V ω. We give a general formula relating the decay of the integrated density of states of H ω at the edges of the almost sure spectrum of H ω to the decay of the integrated density of states of H at the edges of the spectrum of H.
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REFERENCES
M. Aizenman, Localization at weak disorder: Some elementary bounds, Reviews in Mathematical Physics 6:1163-1182 (1994).
M. Aizenman and S. Molchanov, Localization at large disorder and at extreme energies: An elementary derivation, Communications in Mathematical Physics 157:245-278 (1993).
V. Arnold, A. Varchenko, and S. Goussein-Zadé, Singularités des applications différentiables. 2. Monodromie et comportement asymptotique des intégrales (Editions MIR, Moscous, 1986).
H. L. Cycon, R. G. Froese, W. Kirsch, and B. Simon, Schrödinger Operators (Springer Verlag, Berlin, 1987).
A. Dembo and O. Zeitouni, Large devition techniques and applications (Jones and Bartlett Publishers, Boston, 1992).
B. Helffer and J. Sjöstrand, On diamagnetism and the De Hass-Van Alphen effect, Annales de l'Institut Henri Poincaré, Série Physique Théorique 52:303-375 (1990).
L. Hörmander, The Analysis of Linear Partial Differential Operators (Springer Verlag, Heidelberg, 1983).
W. Kirsch and B. Simon, Lifshits tails for the Anderson model, Journal of Statistical Physics 38:65-76 (1985).
F. Klopp, Work in progress.
F. Klopp, Internal Lifshits tails for random perturbations of periodic Schrödinger operators. Preprint, (Université Paris-Nord, Villetaneuse, 1997). (see also Math. Phys. Archive: preprint 97-81 (http://rene.ma.utexas.edu/mp_arc/)).
J. N. Mather, On Nirenberg's proof of Malgrange's preparation theorem, in Proceedings of Liverpool Singularities-Symposium I, number 192 in Lecture Notes in Mathematics, (Springer Verlag, Berlin, 1971).
G. Mezincescu, Internal Lifshits singularities of disordered finite-difference Schrödinger operators, Communications in Mathematical Physics 103:107-116 (1986).
L. Pastur and A. Figotin, Spectra of Random and Almost Periodic Operators (Springer Verlag, Berlin, 1992).
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. IV: Analysis of Operators (Academic Press, New York, 1978).
B. Simon, Lifshits tails for the Anderson model, Journal of Statistical Physics 38:65-76 (1985).
B. Simon, Internal lifshits tails, Journal of Statistical Physics 46:911-918 (1987).
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Klopp, F. Band Edge Behavior of the Integrated Density of States of Random Jacobi Matrices in Dimension 1. Journal of Statistical Physics 90, 927–947 (1998). https://doi.org/10.1023/A:1023293423978
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DOI: https://doi.org/10.1023/A:1023293423978