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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As stated before, we often look at random maps as random metric spaces. Geodesics (or shortest paths) in these spaces then play a crucial part for a study of some geodesics in random maps and their scaling limits). Here are some simulations of geodesic cliques in various random maps. Notice that the geodesics from different vertices toward the same vertex have a tendency to merge before reaching their goal. In fact, Le Gall showed that this property always happens in a large plane quadrangulation, and we later generalized this result to quadrangulations of any orientable surface.