  We study the geodesic two- and three-point functions of random weighted cubic
maps, which are obtained by assigning random edge lengths to random cubic
planar maps. Explicit expressions are obtained by taking limits of recently
established bivariate multi-point functions of general planar maps. We give an
alternative interpretation of the two-point function in terms of an Eden model
exploration process on a random planar triangulation. Finally, the scaling
limits of the multi-point functions are studied, showing in particular that the
two- and three-point functions of the Brownian map are recovered as the number
of faces is taken to infinity.
