Jérémie Bettinelli École polytechnique Laboratoire d'informatique (LIX) 91128 Palaiseau Cedex FRANCE E-mail: firstname « . » lastname « at » normalesup « . » org Office: 2023 Phone: (+33) (0)1 77 57 80 61

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These simulations were realized with Mireille Bousquet-Mélou, Éric Fusy and Kilian Raschel. They represent maps that are chosen uniformly at random among all bipolar oriented triangulations of a given size. A bipolar oriented triangulation is a map with only faces of degree 3 satisfying the following conditions:

• Two neighboring vertices (vertices connected by an edge of the map) are distinguished and called north pole and south pole;
• The edges are oriented in such a way that no egde enters the south pole, no edge leaves the north pole, every vertex distinct from the poles has at least one edge entering and one leaving, and no oriented loops exist.