  It is unknown how far dust growth can proceed by coagulation. Obstacles to
collisional growth are the fragmentation and bouncing barriers. However, in all
previous simulations of the dust-size evolution in protoplanetary disks, only
the mean collision velocity has been considered, neglecting that a small but
possibly important fraction of the collisions will occur at both much lower and
higher velocities. We study the effect of the probability distribution of
impact velocities on the collisional dust growth barriers. Assuming a
Maxwellian velocity distribution for colliding particles to determine the
fraction of sticking, bouncing, and fragmentation, we implement this in a
dust-size evolution code. We also calculate the probability of growing through
the barriers and the growth timescale in these regimes. We find that the
collisional growth barriers are not as sharp as previously thought. With the
existence of low-velocity collisions, a small fraction of the particles manage
to grow to masses orders of magnitude above the main population. A particle
velocity distribution softens the fragmentation barrier and removes the
bouncing barrier. It broadens the size distribution in a natural way, allowing
the largest particles to become the first seeds that initiate sweep-up growth
towards planetesimal sizes.
