Drilling holes in the Brownian disk: The Brownian annulus

Understand

We give a new construction of the Brownian annulus based on removing a hull centered at the distinguished point in the free Brownian disk.

• We use this construction to prove that the Brownian annulus is the scaling limit of Boltzmann triangulations with two boundaries.
• We also prove that the space obtained by removing hulls centered at the two distinguished points of the Brownian sphere is a Brownian annulus.
• Our proofs rely on a detailed analysis of the peeling by layers algorithm for Boltzmann triangulations with a boundary.