Jules Duhamel

An explicit, circle-packed version of the Brooks-Makover model

The breakthrough of Mirzakhani on the Weil-Petersson model generated a lot of interest in random hyperbolic geometry. Three models gather most of the attention. We introduce a new version of one of them, the Brooks-Makover model. This new model is built using circle-packing theory. We compute important quantities of the model (circle perimeter, systole, short-length spectrum) and explain why the model is explicit, as opposed to the Brooks-Makover model. We show that the Teichmüller distance between the circle-packed model and the Brooks-Makover model is bounded.