Multi-particle eigenvalue concentration bounds

In this chapter we begin our analysis of localization in multi-particle Anderson tight-binding models with interaction. We already mentioned that the principal difficulty encountered when working with multi-particle systems is the structure of the external random potential term (3.3) in the Hamiltonian combined with the presence of interaction between particles (see Eq. (3.8) below). To tackle this obstacle, we develop a multi-particle version of the MSA (in short, the MPMSA) by scrutinizing and—when necessary—modifying the subsequent steps of the single-particle MSA scheme.