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We report results of large-scale Monte Carlo simulations ofsuperfluid--insulator transitions in commensurate 2D bosonic systems. In thecase of off-diagonal disorder (quantum percolation), we find that thetransition is to a gapless incompressible insulator, and its dynamical criticalexponent is $z=1.65 \pm 0.2$. In the case of diagonal disorder, we prove theconjecture that rare statistical fluctuations are inseparable from criticalfluctuations on the largest scales and ultimately result in the crossover tothe generic universality class (apparently with $z=2$). However, even at strongdisorder, the universal behavior sets in only at very large space-timedistances. This explains why previous studies of smaller clusters mimicked adirect superfluid--Mott-insulator transition.Comment: 6 pages, Latex, 7 figure

Superfluid-Insulator Transition in Commensurate Disordered Bosonic Systems: Large-Scale Worm Algorithm Simulations