Jason Miller

collaborators

5 papers

math.PR2026

Existence and uniqueness of the canonical Brownian motion in non-simple conformal loop ensemble gaskets

Jason Miller, Yizheng Yuan

We construct the canonical Brownian motion on the gasket of conformal loop ensembles (CLE $_{I^} º$ ) for $I^º \in (4, 8)$ (which is the range of parameter values in which loops of the CLE$…

math.PR2025

Existence and uniqueness of the conformally covariant geodesic metric on non-simple conformal loop ensemble gaskets

Jason Miller, Yizheng Yuan

We construct the canonical geodesic metric on the gasket of conformal loop ensembles (CLE $_{I^} º$ ) in the regime $I^º \in (4, 8)$ where the loops intersect themselves, each other, and th…

math.PR2025

Existence and uniqueness of the conformally covariant geodesic metric on simple conformal loop ensemble carpets

Jason Miller, Yi Tian

We prove that for each $I^º \in (8/3, 4)$ there exists a geodesic metric on the carpet of a CLE $_{I^} º$ which is canonical in the sense that it is characterized by a certain list of axi…

math.PR2025

Tightness of approximations to metrics on non-simple conformal loop ensemble gaskets

Valeria Ambrosio, Jason Miller, Yizheng Yuan

We study a class of approximation schemes aimed at constructing conformally covariant metrics defined in the gasket of a conformal loop ensemble (CLE $_{I^} º$ ) for $I^º \in (4, 8)$ . This…

math.PR2025

Multiple SLE $_{I^} º$ from CLE $_{I^} º$ for $I^º \in (4, 8)$

Valeria Ambrosio, Jason Miller, Yizheng Yuan

We define multichordal CLE $_{I^} º$ for $I^º \in (4, 8)$ as the conditional law of the remainder of a partially explored CLE $_{I^} º$ . The strands of a multichordal CLE $_{I^} º$ have a random lin…

Existence and uniqueness of the canonical Brownian motion in non-simple conformal loop ensemble gaskets

Existence and uniqueness of the conformally covariant geodesic metric on non-simple conformal loop ensemble gaskets

Existence and uniqueness of the conformally covariant geodesic metric on simple conformal loop ensemble carpets

Tightness of approximations to metrics on non-simple conformal loop ensemble gaskets

Multiple SLEI^​º from CLEI^​º for I^º∈(4,8)

Multiple SLE $_{I^} º$ from CLE $_{I^} º$ for $I^º \in (4, 8)$