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We study several probability distributions relevant to the avalanche dynamicsof elastic interfaces driven on a random substrate: The distribution of size,duration, lateral extension or area, as well as velocities. Results from thefunctional renormalization group and scaling relations involving twoindependent exponents, roughness $\zeta$, and dynamics $z$, are confronted tohigh-precision numerical simulations of an elastic line with short-rangeelasticity, i.e. of internal dimension $d=1$. The latter are based on a novelstochastic algorithm which generates its disorder on the fly. Its precisiongrows linearly in the time-discretization step, and it is parallelizable. Ourresults show good agreement between theory and numerics, both for the criticalexponents as for the scaling functions. In particular, the prediction ${\sf a}= 2 - \frac{2}{d+ \zeta - z}$ for the velocity exponent is confirmed with goodaccuracy.

Distribution of velocities in an avalanche, and related quantities: Theory and numerical verification