Scaling limits for peeling explorations of the Brownian half-plane

Abstract

We construct and study peeling explorations of the Brownian half-plane by successively revealing hulls of fixed radius. We prove that for any peeling process, as the radius of the hulls tends to zero, the sequence of discovered hulls converges to an explicit family of Brownian disks. We also consider the particular case of what we call nearest-neighbour peeling explorations, where the center of each new hull is chosen on the outer boundary of the previously discovered hull, naturally giving rise to an exploration curve. We provide scaling limits results for these curves, jointly with the convergence of the associated boundary-length and volume processes.