Spine representations for non-compact models of random geometry

TL;DR

This paper introduces a unified framework for three key non-compact models of random geometry, enabling analysis of their relationships and proving that hull complements in the Brownian plane are infinite-volume Brownian disks.

Contribution

It provides a unified approach to relate the Brownian plane, Brownian disk, and Brownian half-plane, establishing new connections between these models.

Findings

Complement of hulls in the Brownian plane are infinite-volume Brownian disks.

Unified approach links three main non-compact models of random geometry.

Facilitates analysis of relations between different random geometric models.

Abstract

We provide a unified approach to the three main non-compact models of random geometry, namely the Brownian plane, the infinite-volume Brownian disk, and the Brownian half-plane. This approach allows us to investigate relations between these models, and in particular to prove that complements of hulls in the Brownian plane are infinite-volume Brownian disks.