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We report exact predictions for universal scaling exponents and scalingfunctions associated with the distribution of the maximum collective avalanchepropagation velocities $v_m$ in the mean field theory of the interfacedepinning transition. We derive the extreme value distribution $P(v_m|T)$ forthe maximum velocities in avalanches of fixed duration $T$, and verify theresults by numerical simulation near the critical point. We find that the tailof 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 accountfor the observed power-law distribution of the maximum amplitudes in acousticemission experiments of crystal plasticity, and are also broadly applicable toother systems in the mean-field interface depinning universality class, rangingfrom magnets to earthquakes.

Distribution of maximum velocities in avalanches near the depinning transition