  This paper sets out to study the spectral minimum for operator belonging to
the family of random Schr\"{o}dinger 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.
