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Hatem NAJAR
The spectrum minimum for random Schr\"odinger operators with indefinite sign potentials
(747K, pdf, dvi, ps)

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.