  We study the square-lattice Bose-Hubbard model with bounded random on-site
energies at zero temperature. Starting from a dual representation obtained from
a strong-coupling expansion around the atomic limit, we employ a real-space
block decimation scheme. This approach is non-perturbative in the disorder and
enables us to study the renormalization-group flow of the induced random-mass
distribution. In both insulating phases, the Mott insulator and the Bose glass,
the average mass diverges, signaling short range superfluid correlations. The
relative variance of the mass distribution distinguishes the two phases,
renormalizing to zero in the Mott insulator and diverging in the Bose glass.
Negative mass values in the tail of the distribution indicate the presence of
rare superfluid regions in the Bose glass. The breakdown of self-averaging is
evidenced by the divergent relative variance and increasingly non-Gaussian
distributions. We determine an explicit phase boundary between the Mott
insulator and Bose glass.
