In this talk, I present results and techniques to measure the Hausdorff dimension of two types of random geometries. The first is a generalization of the mating of trees approach. The original mating of trees encodes Liouville Quantum Gravity on the 2-sphere in terms of a correlated Brownian motion describing a pair of random trees. We extended this approach to higher-dimensional correlated Brownian motions, leading to a family of non-planar random graphs that belong to new universality classes of scale-invariant random geometries. The second example of random geometry is the D-random feuilletage, which for D=2 agrees with a family of planar maps, while for D>2, these represent new universality classes of random geometries. We developed numerical methods to efficiently simulate these random graphs and explore their scaling limits through distance measurements, allowing us to estimate Hausdorff dimensions.
Localisation
Salle de séminaire 4B125 (bâtiment Copernic)
5 Boulevard Descartes 77420 Champs-sur-Marne