Localization in the multi-particle tight-binding Anderson model at low energy

We consider the multi-particle tight-binding Anderson model and prove that its lower spectral edge is non-random under some mild assumptions on the inter-particle interaction and the random external potential. We also adapt to the low energy regime the multi-particle multi-scale analysis initially developed by Chulaevsky and Suhov in the high disorder limit, if the marginal probability distribution of the i.i.d. random variables is log-Hölder continuous and we obtain the spectral exponential and strong dynamical localization near the bottom of the spectrum.