  A stochastic theory of gravity is described in which the metric tensor is a
random variable such that the spacetime manifold is a fluctuating physical
system at a certain length scale. A general formalism is described for
calculating probability densities for gravitational phenomena in a
generalization of general relativity (GR), which reduces to classical GR when
the magnitude of the metric fluctuations is negligible. Singularities in
gravitational collapse and in big-bang cosmology have zero probability of
occurring. A model of a self-organized critical universe is described which is
independent of its initial conditions.
