Quantum Geometry and Diffusion
  We study the diffusion equation in two-dimensional quantum gravity, and show that the spectral dimension is two despite the fact that the intrinsic Hausdorff dimension of the ensemble of two-dimensional geometries is very different from two. We determine the scaling properties of the quantum gravity averaged diffusion kernel. 
J. Ambjorn (1), K. N. Anagnostopoulos (1), T. Ichihara (2), L. Jensen   (1), Y. Watabiki (2) ((1) Niels Bohr, (2) Tokyo Inst...