  We report exact predictions for universal scaling exponents and scaling
functions associated with the distribution of the maximum collective avalanche
propagation velocities $v_m$ in the mean field theory of the interface
depinning transition. We derive the extreme value distribution $P(v_m|T)$ for
the maximum velocities in avalanches of fixed duration $T$, and verify the
results by numerical simulation near the critical point. We find that the tail
of the distribution of maximum velocity for an arbitrary avalanche duration,
$v_m$, scales as $P(v_m)\sim v_m^{-2}$ for large $v_m$. These results account
for the observed power-law distribution of the maximum amplitudes in acoustic
emission experiments of crystal plasticity, and are also broadly applicable to
other systems in the mean-field interface depinning universality class, ranging
from magnets to earthquakes.
