 05366 Hatem NAJAR
 The spectrum minimum for random Schr\"odinger operators with indefinite sign potentials
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Oct 24, 05

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Abstract. This paper sets out to study the spectral minimum for operator
belonging to the family of random Schr\"odinger operators of the
form $H_{\lambda,\omega}=\Delta+W_{\text{per}}+\lambda
V_{\omega}$, where we suppose that $V_{\omega}$ is of Anderson type
and the single site is assumed to be with an indefinite sign.
Under some assumptions we prove that there exists $\lambda_0>0$
such that for any $\lambda \in [0,\lambda_0]$, the minimum of the
spectrum of $H_{\lambda,\omega}$ is obtained by a given
realization of the random variables.
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