Boundaries of random triangulation of a disk
Maxim Krikun · Discrete Mathematics and Applications · 2004
We consider random triangulations of a disk with k holes and N triangles as N → ∞. The coefficient λ m , λ > 0, is assigned to a triangulation with the total number of boundary edges equal to m . In the case of two boundaries, we separate three domains of variation of the parameter λ , and in each of them find the limit joint distribution of boundary lengths. For a greater number of boundaries, we give an algorithm to calculate the generating functions for the number of multi-rooted triangulations depending of the number of triangles and the lengths of boundaries. In Appendix, we discuss the relation between multi-rooted triangulations and unrooted triangulations, and give analogues of limit distributions for unrooted triangulations.