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math.PR2025
Ancestral diversity in fragmentation trees
Bénédicte Haas, Grégory Miermont
In a deterministic or random tree, a notion of ancestral diversity can be defined as follows. Sample independently groups of leaves and count the number of distinc…
math.PR2025
The snake in the Brownian sphere
Omer Angel, Emmanuel Jacob, Brett Kolesnik +1
The Brownian sphere is a random metric space, homeomorphic to the two-dimensional sphere, which arises as the universal scaling limit of many types of random planar maps. The direc…
math.PR2025
The scaling limit of planar maps with large faces
Nicolas Curien, Grégory Miermont, Armand Riera
We prove that large Boltzmann stable planar maps of index converge in the scaling limit towards a random compact metric space that we construct explici…