Constructing the Brownian sphere from a continuum random unicycle

Fuente: arXiv
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Main Author: Mourichoux, Mathieu
Format: Preprint
Published: 2025
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_version_ 1866917073732501504
author Mourichoux, Mathieu
author_facet Mourichoux, Mathieu
contents We give an explicit construction of the Brownian sphere biased by the distance between two distinguished points, which is based on the Miermont bijection for quadrangulations. We then describe various conditionings of this object, which are related to Voronoï cells in the Brownian sphere. In particular, we give a new construction of the Brownian sphere with two distinguished points at a fixed distance. We also use this construction to derive a new representation of the bigeodesic Brownian plane.
format Preprint
id arxiv_https___arxiv_org_abs_2511_08524
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Constructing the Brownian sphere from a continuum random unicycle
Mourichoux, Mathieu
Probability
60D05 (Primary), 60C05 (Secondary)
We give an explicit construction of the Brownian sphere biased by the distance between two distinguished points, which is based on the Miermont bijection for quadrangulations. We then describe various conditionings of this object, which are related to Voronoï cells in the Brownian sphere. In particular, we give a new construction of the Brownian sphere with two distinguished points at a fixed distance. We also use this construction to derive a new representation of the bigeodesic Brownian plane.
title Constructing the Brownian sphere from a continuum random unicycle
topic Probability
60D05 (Primary), 60C05 (Secondary)
url https://arxiv.org/abs/2511.08524