# The number of spanning clusters of the uniform spanning tree in three dimensions

10 Mar 2020 Angel Omer Croydon David A. Hernandez-Torres Sarai Shiraishi Daisuke

Let ${\mathcal U}_{\delta}$ be the uniform spanning tree on $\delta \mathbb{Z}^{3}$. A spanning cluster of ${\mathcal U}_{\delta}$ is a connected component of the restriction of ${\mathcal U}_{\delta}$ to the unit cube $[0,1]^{3}$ that connects the left face $\{ 0 \} \times [0,1]^{2}$ to the right face $\{ 1 \} \times [0,1]^{2}$... (read more)

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