  Mechanical deformation of amorphous solids can be described as consisting of
an elastic part in which the stress increases linearly with strain, up to a
yield point at which the solid either fractures or starts deforming
plastically. It is well established, however, that the apparent linearity of
stress with strain is actually a proxy for a much more complex behavior, with a
microscopic plasticity that is reflected in diverging nonlinear elastic
coefficients. Very generally, the complex structure of the energy landscape is
expected to induce a singular response to small perturbations. In the athermal
quasistatic regime, this response manifests itself in the form of a scale free
plastic activity. The distribution of the corresponding avalanches should
reflect, according to theoretical mean field calculations (Franz and Spigler,
Phys. Rev. E., 2017, 95, 022139), the geometry of phase space in the vicinity
of a typical local minimum. In this work, we characterize this distribution for
simple models of glass forming systems, and we find that its scaling is
compatible with the mean field predictions for systems above the jamming
transition. These systems exhibit marginal stability, and scaling relations
that hold in the stationary state are examined and confirmed in the elastic
regime. By studying the respective influence of system size and age, we suggest
that marginal stability is systematic in the thermodynamic limit.
