SIMPLICIAL GRAVITY IN DIMENSION GREATER-THAN-2

We consider two issues in the DT model of quantum gravity. First, it i s shown that the triangulation space for D > 3 is dominated by triangu lations containing a single singular (D - 3)-simplex composed of verti ces with divergent dual volumes. Second we study the ergodicity of cur rent simulation algorithms. Results from runs conducted close to the p hase transition of the four-dimensional theory are shown. We see no st rong indications of ergodicity breaking in the simulation and our data support recent claims that the transition is most probably first orde r. Furthermore, we show that the critical properties of the system are determined by the dynamics of remnant singular vertices.