Scale-invariant random geometries from mating of trees

Alicia Castro

In this talk, I present new results on the search for scale-invariant random geometries in the context of Quantum Gravity. To uncover new universality classes of such geometries, we generalized the mating of trees approach, which encodes Liouville Quantum Gravity on the 2-sphere in terms of a correlated Brownian motion describing a pair of random trees. We extended this approacyouh 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. We developed a numerical method to efficiently simulate these random graphs and explore their scaling limits through distance measurements, allowing us to estimate Hausdorff dimensions in the two- and three-dimensional settings.

Keywords:
Quantum Gravity, Random Geometry

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