Growth-fragmentation in Liouville quantum gravity via planar excursions

Growth-fragmentation processes are examples of branching structures which may help to understand some features of random geometry. An instance of such a connection was revealed in a work of Bertoin, Budd, Curien and Kortchemski, where a remarkable branching structure appears in the scaling limit from a peeling exploration of some random planar maps. More recently, Miller, Sheffield and Werner constructed the same branching structure directly in the continuum, in the setting of Liouville quantum gravity. The purpose of the talk is to propose a different route, going through planar Brownian excursions. We first prove that similar objects appear in this context, and then relate the two approaches through the celebrated mating-of-trees.

The talk is partly based on joint works with Élie Aïdékon (Fudan University), and with Ellen Powell (Durham University) and Alexander Watson (UCL).