15. November 2025

Triangulation associated to Weil-Petersson random surface

Figure An embedding in 3D of the triangulation associated to a Weil-Petersson random surface with 30000 cusps.

Figure The triangulation associated to a Weil-Petersson random surface with 29067 cusps.

Figure The triangulation associated to a Weil-Petersson random surface with 35320 cusps.

References

[1] Rivin, Igor. Intrinsic geometry of convex ideal polyhedra in hyperbolic 3-space. Lecture Notes in Pure and Applied Mathematics (1994): 275-275.

[2] Budd, Timothy. “Irreducible metric maps and Weil–Petersson volumes.” Communications in Mathematical Physics 394, no. 2 (2022): 887-917.

[3] Charbonnier, Séverin, François David, and Bertrand Eynard. “Local properties of the random Delaunay triangulation model and topological 2D gravity.” arXiv preprint arXiv:1701.02580 (2017).

[4] Budd, Timothy, and Nicolas Curien. Random punctured hyperbolic surfaces & the Brownian sphere. arXiv preprint arXiv:2508.18792 (2025).