Real-space renormalization study of disordered interacting bosons

We study a real-space renormalization group for disordered, interacting bosons at zero temperature in one and two dimensions. In the absence of disorder at commensurate density we find a superfluid--Mott insulator transition that is unaffected by the addition of weak disorder, i.e., disorder is weakly irrelevant at the Mott-superfluid transition. Above a threshold disorder a gapless insulating phase---the ``Bose glass''---intervenes.