  We show how gravitational actions, in particular the Einstein-Hilbert action,
can be obtained from additional terms in Yang-Mills matrix models. This is
consistent with recent results on induced gravitational actions in these matrix
models, realizing space-time as 4-dimensional brane solutions. It opens up the
possibility for a controlled non-perturbative description of gravity through
simple matrix models, with interesting perspectives for the problem of vacuum
energy. The relation with UV/IR mixing and non-commutative gauge theory is
discussed.
