8 papers · 1 filter
On the distortion of random triangulations
Jason Miller, Julian Ransford, Fredy Yip
For each , let be a uniformly random (rooted, Type I) triangulation of the sphere with vertices, viewed as a metric space equipped with its graph distan…
The conformally invariant metric on CLE III: uniqueness
Emmanuel Kammerer, Konstantinos Kavvadias, Jason Miller +1
This paper is the third and final article in a series of papers constructing the canonical conformally invariant metric on the set of loops of the conformal loop ensemble (CLE) wit…
The conformally invariant metric on CLE II: existence of geodesics
Emmanuel Kammerer, Konstantinos Kavvadias, Jason Miller +1
We continue our study of the conformal loop ensemble (CLE) with parameter , the critical threshold at or below which the loops are simple and disjoint, touching neither each o…
Quasisymmetric rigidity of the Brownian sphere
Jason Miller, Yi Tian
The Brownian sphere, also known as the Brownian map, is a canonical random metric measure space homeomorphic to the two-dimensional sphere . It can be interpreted as t…
The conformal dimension of the Brownian tree is one
Jason Miller, Yi Tian
The Brownian tree, also known as the continuum random tree, is a canonical random compact, geodesic -tree that arises as the universal scaling limit for numerous models…
The scaling limit of random walk and the intrinsic metric on planar critical percolation
Irina Đanković, Maarten Markering, Jason Miller +1
We consider critical site percolation () on the triangular lattice in two dimensions. We show that the simple random walk on the clusters of open vertices c…
Minkowski content construction of the CLE gasket measure
Jason Miller, Yizheng Yuan
We show that the canonical conformally covariant measure on the conformal loop ensemble (CLE) gasket/carpet, previously constructed indirectly by the first co-author and Schoug…
Liouville quantum gravity as a mating of trees
Bertrand Duplantier, Jason Miller, Scott Sheffield
There is a simple way to "glue together" a coupled pair of continuum random trees (CRTs) to produce a topological sphere. The sphere comes equipped with a measure and a space-filli…