Universal fluctuations and extreme statistics of avalanches near the depinning transition

We derive exact predictions for universal scaling exponents and scaling functions associated with the statistics of maximum velocities v_m during avalanches described by the mean-field theory of the interface depinning transition. In particular, we find a robust power-law regime in the statistics of maximum events that can explain the observed distribution of the peak amplitudes in acoustic emission experiments of crystal plasticity. Our results are expected to be broadly applicable to a broad range of systems in the mean-field interface depinning universality class, ranging from magnets to earthquakes.