  Interfaces pinned by quenched disorder are often used to model jerky
self-organized critical motion. We study static avalanches, or shocks, defined
here as jumps between distinct global minima upon changing an external field.
We show how the full statistics of these jumps is encoded in the
functional-renormalization-group fixed-point functions. This allows us to
obtain the size distribution P(S) of static avalanches in an expansion in the
internal dimension d of the interface. Near and above d=4 this yields the
mean-field distribution P(S) ~ S^(-3/2) exp(-S/[4 S_m]) where S_m is a
large-scale cutoff, in some cases calculable. Resumming all 1-loop
contributions, we find P(S) ~ S^(-tau) exp(C (S/S_m)^(1/2) -B/4 (S/S_m)^delta)
where B, C, delta, tau are obtained to first order in epsilon=4-d. Our result
is consistent to O(epsilon) with the relation tau = 2-2/(d+zeta), where zeta is
the static roughness exponent, often conjectured to hold at depinning. Our
calculation applies to all static universality classes, including random-bond,
random-field and random-periodic disorder. Extended to long-range elastic
systems, it yields a different size distribution for the case of contact-line
elasticity, with an exponent compatible with tau=2-1/(d+zeta) to
O(epsilon=2-d). We discuss consequences for avalanches at depinning and for
sandpile models, relations to Burgers turbulence and the possibility that the
above relations for tau be violated to higher loop order. Finally, we show that
the avalanche-size distribution on a hyper-plane of co-dimension one is in
mean-field (valid close to and above d=4) given by P(S) ~ K_{1/3}(S)/S, where K
is the Bessel-K function, thus tau=4/3 for the hyper plane.
