Hatem NAJAR
The spectrum minimum for random Schr\"odinger operators with indefinite sign potentials
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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.