MINBU DISTRIBUTION OF 2-DIMENSIONAL QUANTUM-GRAVITY - SIMULATION RESULT AND SEMICLASSICAL ANALYSIS

We analyze the MINBU distribution of two-dimensional quantum gravity. New data of R(2)-gravity by the Monte Carlo simulation and its theoret ical analysis by the semiclassical approach are presented. In the dist ribution, the cross-over phenomenon takes place at some size of the ba by universe where the randomness competes with the smoothing (or rough ening) force of R(2)-term. The dependence on the central charge c(m) a nd on the R(2)-coupling are explained for R(2)-gravity, which includes the ordinary 2d quantum gravity. The R(2)-Liouville solution plays th e central role in the semiclassical analysis. A total derivative term (surface term) and the infrared regularization play important roles. T he surface topology is that of a sphere.