  In infinite dimension, many-body systems of pairwise interacting particles
provide exact analytical benchmarks for features of amorphous materials, such
as the stress-strain curve of glasses under quasistatic shear. Here, instead of
a global shear, we consider an alternative driving protocol as recently
introduced in Ref. [1], which consists of randomly assigning a constant local
displacement on each particle, with a finite spatial correlation length. We
show that, in the infinite-dimension limit, the mean-field dynamics under such
a random forcing is strictly equivalent to that under global shear, upon a
simple rescaling of the accumulated strain. Moreover, the scaling factor is
essentially given by the variance of the relative local displacements on
interacting pairs of particles, which encodes the presence of a finite spatial
correlation. In this framework, global shear is simply a special case of a much
broader family of local forcing, that can be explored by tuning its spatial
correlations. We discuss specifically the implications on the quasistatic
driving of glasses -- initially prepared at a replica-symmetric equilibrium --
and how the corresponding 'stress-strain'-like curves and the elastic moduli
can be rescaled onto their quasistatic-shear counterparts. These results hint
at a unifying framework for establishing rigourous analogies, at the mean-field
level, between different driven disordered systems.
