Cillian Doherty

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math.PR2025

The square summability of the CLE complementary component diameters

Cillian Doherty, Jason Miller

We show that the sum of the squares of the diameters of the complementary connected components of the CLE $_{I^} º$ carpet/gasket is almost surely finite for $Îº\in (8/3, 4) \cup (4, 8)…

math.PR2024

Connectivity of the adjacency graph of complementary components of the SLE fan

Cillian Doherty, Konstantinos Kavvadias, Jason Miller

Suppose that $h$ is an instance of the Gaussian free field (GFF) on a simply connected domain $D \subseteq C$ and $x, y \in \partial D$ are distinct. Fix $I^º \in (0, 4)$ and…