Orateur
Description
We study the branching structure induced by a space-filling SLE(6) exploration of the quantum disc with matching parameter. We prove that it can be described as one of the growth-fragmentation processes introduced by Bertoin, Budd, Curien and Kortchemski in the context of planar maps. Importantly, our arguments are elementary, relying only on planar Brownian motion, and requiring no prior knowledge on LQG, once translated through the mating of trees. To this end, we develop new elements of excursion theory for cone excursions of Brownian motion and explore their connections to stable Lévy processes. This set of tools provides new elementary proofs of some of the key properties of the above SLE/LQG coupling. This talk is based on joint work with Ellen Powell (Durham) and Alex Watson (UCL).
