The spectrum minimum for random Schrödinger operators with indefinite sign potentials

This paper sets out to study the spectral minimum for operator belonging to the family of random Schrödinger operators of the form Hλ,ω = −∆+Wper + λVω, where we suppose that Vω is of Anderson type and the single site is assumed to be with an indefinite sign. Under some assumptions we prove that there exists λ0 > 0 such that for any λ ∈ [0, λ0], the minimum of the spectrum of Hλ,ω is obtained by a given realization of the random variables. 2000 Mathematics Subject Classification:81Q10, 35P05, 37A30,47F05.