Localization in multiparticle Anderson models with weak interaction

We prove that spectral and strong dynamical localization occurs in the one-dimensional multiparticle Anderson model with weak interaction in the continuous configuration space. To obtain these results, the interaction amplitude must be sufficiently small. The general strategy relies on an estimate in the framework of multiscale analysis. In fact, we prove that the multiscale analysis estimates for the single-particle model are unchanged in passing to multiparticle systems if the interparticle interaction is sufficiently small. The only condition imposed on the probability distribution of the external potential, which is a random field of independent identically distributed random quantities, is that it must be logarithmically continuous in the Hölder sense.