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Название: On the Large-Coupling-Constant Behavior of the Liapunov Exponent in a Binary Alloy
Авторы: Martinelli F., Micheli L.
Journal of Statistical Physics, Vol. 48, Nos. 1/2, 1987, p. 1-18.
We consider the usual one-dimensional tight-binding Anderson model with the random potential taking only two values, 0 and Lam, with probability p and 1 - p, 0 < p < 1. We show that the Liapunov exponent y_Lam(E), Ee R, diverges as Lam -> oo uniformly in the energy E. Using a result of Carmona, Klein, and Martinelli, this proves that for Lam large enough, the integrated density of states is singular continuous. We also compute explicitly the exact asymptotics for a dense set of energies and we compare the results with numerical simulations.