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Lifshitz tails for periodic plus random potentials. (English) Zbl 0629.60077

We prove that the integrated density of states p(\(\lambda)\) for a potential \(W_{\omega}=V_{per}+V_{\omega}\) has Lifshitz tails where \(V_{per}\) is a periodic potential with reflection symmetry and \(V_{\omega}\) is a random potential, e.g., of the form \(V_{\omega}=\sum q_ i(\omega)f(x-i)\).

MSC:

60H25 Random operators and equations (aspects of stochastic analysis)
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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