Scaling Structures in Four-dimensional Simplicial Gravity
  Four-dimensional(4D) spacetime structures are investigated using the concept of the geodesic distance in the simplicial quantum gravity. On the analogy of the loop length distribution in 2D case, the scaling relations of the boundary volume distribution in 4D are discussed in various coupling regions i.e. strong-coupling phase, critical point and weak-coupling phase. In each phase the different scaling relations are found. 
H. S. Egawa, T. Hotta, T. Izubuchi, N. Tsuda and T. Yukawa