  A large class of two dimensional quantum gravity theories of
Jackiw-Teitelboim form have a description in terms of random matrix models.
Such models, treated fully non-perturbatively, can give an explicit and
tractable description of the underlying ``microstate'' degrees of freedom. They
play a prominent role in regimes where the smooth geometrical picture of the
physics is inadequate. This is shown using a natural tool for extracting the
detailed microstate physics, a Fredholm determinant ${\rm
det}(\mathbf{1}{-}\mathbf{ K})$. Its associated kernel $K(E,E^\prime)$ can be
defined explicitly for a wide variety of JT gravity theories. To illustrate the
methods, the statistics of the first several energy levels of a
non-perturbative definition of JT gravity are constructed explicitly using
numerical methods, and the full quenched free energy $F_Q(T)$ of the system is
computed for the first time. These results are also of relevance to quantum
properties of black holes in higher dimensions.
