Title: Classification of scaling limits of uniform quadrangulations with a boundary
Abstract: We study noncompact scaling limits of uniform random planar quadrangulations with a boundary when their size tends to infinity.Depending on the asymptotic behavior of the boundary size and the choice of the scaling factor, we observe different limiting metric spaces.Among well-known objects like the Brownian plane or the self-similar continuum random tree, we construct two new one-parameter families of metric spaces that appear as scaling limits: the Brownian half-plane with skewness parameter θ and the infinitevolume Brownian disk of perimeter σ .We also obtain various coupling and limit results clarifying the relation between these objects.