Constructing the Brownian sphere from a continuum random unicycle
Probability
2025-11-12 v1
Abstract
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 Vorono\"i 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.
Cite
@article{arxiv.2511.08524,
title = {Constructing the Brownian sphere from a continuum random unicycle},
author = {Mathieu Mourichoux},
journal= {arXiv preprint arXiv:2511.08524},
year = {2025}
}
Comments
53 pages, 6 figures. Comments are welcome !