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We calculate numerically the sizes S of jumps (avalanches) betweensuccessively pinned configurations of an elastic line (d=1) or interface (d=2),pulled by a spring of (small) strength m^2 in a random-field landscape. Weobtain strong evidence that the size distribution, away from the small-scalecutoff, takes the form P(S) = p(S/S_m) <S>/S_m^2, where S_m:=<S^2>/(2<S>),proportional to m^(-d-zeta), is the scale of avalanches, and zeta the roughnessexponent at the depinning transition. Measurement of the scaling function f(s):= s^tau p(s) is compared with the predictions from a recent Functional RG(FRG) calculation, both at mean-field and one-loop level. The avalanche-sizeexponent tau is found in good agreement with the conjecture tau = 2-2/(d+zeta), recently confirmed to one loop via the FRG. The function f(s)exhibits a shoulder and a stretched exponential decay at large s, with ln f(s)proportional to - s^delta, and delta approximately 7/6 in d=1. The functionf(s), universal ratios of moments, and the generating function <exp(lambda s)>are found in excellent agreement with the one-loop FRG predictions. Thedistribution of local avalanche sizes, i.e. of the jumps of a subspace of themanifold of dimension d', is also computed and compared to our FRG predictions,and to the conjecture tau' =2- 2/(d'+zeta).

Avalanche-size distribution at the depinning transition: A numerical test of the theory