Multi-point functions of weighted cubic maps

Understand

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.