On the exponential bound in four dimensional simplicial gravity
  Simplicial quantum gravity has been proposed as a regularization for four dimensional quantum gravity. The partition function is constructed by performing a weighted sum over all triangulations of the 4-sphere. The model is well-defined only if the number of such triangulations consisting of $N$ simplexes is exponentially bounded. Numerical simulations seem so far to favor such a bound. 
J. Ambjorn and J. Jurkiewicz