4 papers
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…
The conformally invariant metric on CLE I: subsequential limits of the non-simple CLE graph metric
Emmanuel Kammerer, Konstantinos Kavvadias, Jason Miller +1
We consider the conformal loop ensemble (CLE) with the parameter , the critical value at or below which the loops are simple and do not intersect each other or the domain boun…
Existence and uniqueness of the conformally covariant geodesic metric on simple conformal loop ensemble carpets
Jason Miller, Yi Tian
We prove that for each there exists a geodesic metric on the carpet of a CLE which is canonical in the sense that it is characterized by a certain list of axiom…