# Spine representations for non-compact models of random geometry

@article{LeGall2021SpineRF, title={Spine representations for non-compact models of random geometry}, author={Jean-François Le Gall and Armando Riera}, journal={Probability Theory and Related Fields}, year={2021} }

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.

## 7 Citations

### Isoperimetric inequalities in the Brownian plane

- MathematicsThe Annals of Probability
- 2022

We consider the model of the Brownian plane, which is a pointed non-compact random metric space with the topology of the complex plane. The Brownian plane can be obtained as the scaling limit in…

### The Brownian disk viewed from a boundary point.

- Mathematics
- 2020

We provide a new construction of Brownian disks in terms of forests of continuous random trees equipped with nonnegative labels corresponding to distances from a distinguished point uniformly…

### Geodesic stars in random geometry

- Mathematics
- 2021

A point of a metric space is called a geodesic star with m arms if it is the endpoint of m disjoint geodesics. For every m ∈ { 1 , 2 , 3 , 4 } , we prove that the set of all geodesic stars with m…

### GEODESICS IN THE BROWNIAN MAP: STRONG CONFLUENCE AND GEOMETRIC STRUCTURE

- Mathematics
- 2020

We study geodesics in the Brownian map $(\mathcal{S}, d, \nu)$, the random metric measure space which arises as the Gromov-Hausdorff scaling limit of uniformly random planar maps. Our results apply…

### microscopic derivation of coupled SPDE’s with a

- Mathematics
- 2022

. This paper is concerned with the relationship between forward–backward stochastic Volterra integral equations (FBSVIEs, for short) and a system of (nonlocal in time) path dependent partial…

### ISOPERIMETRIC INEQUALITIES IN THE BROWNIAN PLANE BY ARMAND RIERA

- Mathematics
- 2022

We consider the model of the Brownian plane, which is a pointed noncompact random metric space with the topology of the complex plane. The Brownian plane can be obtained as the scaling limit in…

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We provide a new construction of Brownian disks in terms of forests of continuous random trees equipped with nonnegative labels corresponding to distances from a distinguished point uniformly…

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