  The similarity in mechanical properties of dense active matter and sheared
amorphous solids has been noted in recent years without a rigorous examination
of the underlying mechanism. We develop a mean-field model that predicts that
their critical behavior should be equivalent in infinite dimensions, up to a
rescaling factor that depends on the correlation length of the applied field.
We test these predictions in 2d using a new numerical protocol, termed
`athermal quasi-static random displacement', and find that these mean-field
predictions are surprisingly accurate in low dimensions. We identify a general
class of perturbations that smoothly interpolate between the uncorrelated
localized forces that occur in the high-persistence limit of dense active
matter, and system-spanning correlated displacements that occur under applied
shear. These results suggest a universal framework for predicting flow,
deformation, and failure in active and sheared disordered materials.
