ON THE CONNECTION BETWEEN 2D TOPOLOGICAL GRAVITY AND THE REDUCED HERMITIAN MATRIX MODEL

We discuss how concepts such as geodesic length and the volume of spac e-time can appear in 2d topological gravity. We then construct a detai led mapping between the reduced Hermitian matrix model and 2d topologi cal gravity at genus zero. This leads to a complete solution of the co unting problem for planar graphs with vertices of even coordination nu mber. The connection between multi-critical matrix models and multi-cr itical topological gravity at genus zero is studied in some detail. (C ) 1997 Elsevier Science B.V. PACS: 04.60.-m.