Peeling the Brownian half-plane

TL;DR

This paper introduces a new spatial Markov property for the Brownian half-plane, showing that removing a hull preserves its structure and independence, and explores distributional properties and new constructions related to distances from the boundary.

Contribution

It establishes a novel spatial Markov property for the Brownian half-plane and provides new insights into its structure and hull distributional properties.

Findings

Removing a hull yields an independent Brownian half-plane

Distributional properties of boundary-centered hulls are characterized

A new construction of the Brownian half-plane reveals distance information from the boundary

Abstract

We establish a new spatial Markov property of the Brownian half-plane. According to this property, if one removes a hull centered at a boundary point, the remaining space equipped with an intrinsic metric is still a Brownian half-plane, which is independent of the part that has been removed. This is an analog of the well-known peeling procedure for random planar maps. We also investigate several distributional properties of hulls centered at a boundary point, and we provide a new construction of the Brownian half-plane giving information about distances from a half-boundary.