The three-point function of general planar maps

Abstract

We compute the distance-dependent three-point function of general planar maps and of bipartite planar maps, i.e., the generating function of these maps with three marked vertices at prescribed pairwise distances. Explicit expressions are given for maps counted by their number of edges only, or by both their numbers of edges and faces. A few limiting cases and applications are discussed.

33 pages, 12 figures

References in corpus (3)

• The topological structure of scaling limits of large planar maps
• The three-point function of planar quadrangulations
• Trees and spatial topology change in CDT

Cited by in corpus (5)

• Bijective enumeration of planar bipartite maps with three tight boundaries, or how to slice pairs of pants
• On a conjecture by Chapuy about Voronoi cells in large maps
• Large deviation Local Limit Theorems and limits of biconditioned Trees and Maps
• The mesoscopic geometry of sparse random maps
• Random Lévy Looptrees and Lévy Maps