We discuss avalanche and finite size fluctuations in a mesoscopic model to
describe the shear plasticity of amorphous materials. Plastic deformation is
assumed to occur through series of local reorganizations. Yield stress criteria
are random while each plastic slip event induces a quadrupolar long range
elastic stress redistribution. The model is discretized on a regular square
lattice. Shear plasticity can be studied in this context as a depinning dynamic
phase transition. We show evidence for a scale free distribution of avalanches
P(s)∝S−κ with a non trivial exponent κ≈1.25
significantly different from the mean field result κ=1.5. Finite size
effects allow for a characterization of the scaling invariance of the yield
stress fluctuations observed in small samples. We finally identify a population
of precursors of plastic activity and characterize its spatial distribution