EXACT SOLUTION OF DISCRETE 2-DIMENSIONAL R(2) GRAVITY

We exactly solve a special matrix model of dually weighted planar grap hs describing pure two-dimensional quantum gravity with an R(2) intera ction. It permits us to study the intermediate regimes between the gra vitating and hat metric. Flat space is modeled by a regular square lat tice, while localised curvature is introduced through lattice defects, No ''flattening'' phase transition is found with respect to the R(2) coupling: the infrared behaviour of the system is that of pure gravity for any finite R(2) coupling. In the limit of infinite coupling, we a re able to extract a scaling function interpolating between pure gravi ty and a dilute gas of curvature defects on a flat background. We intr oduce and explain some novel techniques concerning our method of large -N character expansions and the calculation of Schur characters on big Young tableaux.