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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…