title: The snake in the Brownian sphere
summary: The Brownian sphere is a random metric space, homeomorphic to the
  two-dimensional sphere, which arises as the universal scaling limit of many
  types of random planar maps. The direct construction of the Brownian sphere is
  via a continuous analogue of the Cori--Vauquelin--Schaeffer (CVS) bijection.
  The CVS bijection maps labeled trees to planar maps, and the continuous version
  maps Aldous' continuum random tree with Brownian labels (the Brownian snake) to
  the Brownian sphere. In this work, we describe the inverse of the continuous
  CVS bijection, by constructing the Brownian snake as a measurable function of
  the Brownian sphere. Special care is needed to work with the orientation of the
  Brownian sphere.
paper_authors._id: 67bd8759fdecc637bd621e6b
paper_authors.name: Omer Angel
paper_authors._id: 67bd8759fdecc637bd621e6c
paper_authors.name: Emmanuel Jacob
paper_authors._id: 67bd8759fdecc637bd621e6d
paper_authors.name: Brett Kolesnik
paper_authors._id: 67bd8759fdecc637bd621e6e
paper_authors.name: Grégory Miermont
paper_title: The snake in the Brownian sphere
paper_summary: The Brownian sphere is a random metric space, homeomorphic to the
  two-dimensional sphere, which arises as the universal scaling limit of many
  types of random planar maps. The direct construction of the Brownian sphere is
  via a continuous analogue of the Cori--Vauquelin--Schaeffer (CVS) bijection.
  The CVS bijection maps labeled trees to planar maps, and the continuous version
  maps Aldous' continuum random tree with Brownian labels (the Brownian snake) to
  the Brownian sphere. In this work, we describe the inverse of the continuous
  CVS bijection, by constructing the Brownian snake as a measurable function of
  the Brownian sphere. Special care is needed to work with the orientation of the
  Brownian sphere.
paper_ai_keywords: Brownian sphere random metric space Cori--Vauquelin--Schaeffer (CVS) bijection planar maps Aldous' continuum random tree Brownian labels Brownian snake measurable function orientation