Towards a Non-Perturbative Renormalization of Euclidean Quantum Gravity

A real space renormalization group technique, based on the hierarchical baby-universe structure of a typical dynamically triangulated manifold, is used to study scaling properties of 2d and 4d lattice quantum gravity. In 4d, the $\beta$-function is defined and calculated numerically. An evidence for the existence of an ultraviolet stable fixed point of the theory is presented