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In the present note, we determine the ground state energy and study theexistence of Lifshitz tails near this energy for some non monotonous alloy typemodels. Here, non monotonous means that the single site potential coming intothe alloy random potential changes sign. In particular, the random operator isnot a monotonous function of the random variables.

Spectral extrema and Lifshitz tails for non monotonous alloy type models