An axiomatic characterization of the Brownian map

Jason Miller, Scott Sheffield⋆

Type: Article

Publication Date: 2021-03-05

Citations: 20

DOI: https://doi.org/10.5802/jep.155

Abstract

The Brownian map is a random sphere-homeomorphic metric measure space obtained by "gluing together" the continuum trees described by the x and y coordinates of the Brownian snake. We present an alternative "breadth-first" construction of the Brownian map, which produces a surface from a certain decorated branching process. It is closely related to the peeling process, the hull process, and the Brownian cactus.

Locations

Journal de l’École polytechnique — Mathématiques - View - PDF
arXiv (Cornell University) - View - PDF
DSpace@MIT (Massachusetts Institute of Technology) - View - PDF
Apollo (University of Cambridge) - View - PDF
French digital mathematics library (Numdam) - View - PDF

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