## Probability Seminar

The uniform spanning tree (UST) on Z^3 is the infinite-volume limit of uniformly chosen spanning trees of large finite subgraphs of Z^3. The main theorem in this talk is the existence of subsequential scaling limits of the UST on Z^3. We get convergence over dyadic subsequences. An essential tool is Wilson’s algorithm, which samples uniform spanning trees by using loop-erased random walks (LERW). This strategy imposes a restriction: results for the scaling limit of 3D LERW constrain the corresponding results for the 3D UST. We will comment on work in progress for the LERW that leads to the full convergence to the scaling limit of the UST.

This talk is based on joint work with Omer Angel, David Croydon, and Daisuke Shiraishi; and work in progress with Xinyi Li and Daisuke Shiraishi.

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Meeting ID: 984 6887 2005

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