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math.PR2025
Constructing the Brownian sphere from a continuum random unicycle
Mathieu Mourichoux
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 t…
math.PR2025
There are no geodesic hubs in the Brownian sphere
Mathieu Mourichoux
A point of a metric space is called a -hub if it is the endpoint of exactly disjoint geodesics, and that the concatenation of any two of these paths is still a geodesic. We…
math.PR2024
The bigeodesic Brownian plane
Mathieu Mourichoux
We introduce and study a random non-compact space called the bigeodesic Brownian plane, and prove that it is the tangent plane in distribution of the Brownian sphere at a point of…