Simplicial Gravity in Dimension Greater than Two

We consider two issues in the DT model of quantum gravity. First, it is shown that the triangulation space for D>3 is dominated by triangulations containing a single singular (D-3)-simplex composed of vertices with divergent dual volumes. Second we study the ergodicity of current simulation algorithms. Results from runs conducted close to the phase transition of the four-dimensional theory are shown. We see no strong indications of ergodicity br eaking in the simulation and our data support recent claims that the transition is most probably first order. Furthermore, we show that the critical properties of the system are determined by the dynamics of remnant singular vertices.