  We consider the multi-particle Anderson tight-binding 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-H\"older
continuous and obtain the spectral exponential and strong dynamical
localization near the bottom of the spectrum.
