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math.PR2019
On quasisymmetric embeddings of the Brownian map and continuum trees
Sascha Troscheit
The Brownian map is a model of random geometry on the sphere and as such an important object in probability theory and physics. It has been linked to Liouville Quantum Gravity and…
math.MG2019
Assouad spectrum thresholds for some random constructions
Sascha Troscheit
The Assouad dimension of a metric space determines its extremal scaling properties. The derived notion of the Assouad spectrum fixes relative scales by a scaling function to obtain…