Interacting electrons in a random medium

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In this talk, we present a simple model of one dimensional interacting electrons in a disordered environment and describe its thermodynamic limit.We shall describe both the ground state energy per particle and the ground state itself.Our main parameter to control the system is the density of particles (or equivalently the density of random scatterers): we assume the density of particles to be small (or equivalently thedensity of random scatterers to be large).The electrons interact through a repulsive potential. We will in particular be interested in the effect of the interaction on the localization properties of the ground state. The results were obtained in collaboration with N.Veniaminov.