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Quantifying the universality of avalanche observables beyond criticalexponents is of current great interest in theory and experiments. Here, weimprove the characterization of the spatio-temporal process inside avalanchesin the universality class of the depinning of elastic interfaces in randommedia. Surprisingly, at variance with the temporal shape, the spatial shape ofavalanches has not yet been predicted. In part this is due to a lack of ananalytically tractable definition: how should the shapes be centered? Here weintroduce such a definition, accessible in experiments, and study the meanspatial shape of avalanches at fixed size centered around their starting point(seed). We calculate the associated universal scaling functions, both in amean-field model and beyond. Notably, they are predicted to exhibit a cuspsingularity near the seed. The results are in good agreement with a numericalsimulation of an elastic line.

Universality in the mean spatial shape of avalanches