  We study the short distance behaviour of euclidean quantum gravity in the
light of Weinberg's asymptotic safety scenario. Implications of a non-trivial
ultraviolet fixed point are reviewed. Based on an optimised renormalisation
group, we provide analytical flow equations in the Einstein-Hilbert truncation.
A non-trivial ultraviolet fixed point is found for arbitrary dimension. We
discuss a bifurcation pattern in the spectrum of eigenvalues at criticality,
and the large dimensional limit of quantum gravity. Implications for quantum
gravity in higher dimensions are indicated.
