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The scaling limit of the uniform spanning tree
Probability| Speaker: | Asaf Nachmias, Tel Aviv University |
| Location: | 2112 MSB |
| Start time: | Thu, Oct 8 2026, 1:10PM |
Description
We show that the Brownian continuum random tree is the Gromov-Hausdorff-Prohorov scaling limit of the uniform spanning tree on high-dimensional graphs including the d-dimensional torus $Z_n^d$ with $d > 4$, the hypercube $\{0,1\}^n$ , and transitive expander graphs. Several corollaries for associated quantities are then deduced: convergence in distribution of the rescaled diameter, height and simple random walk on these uniform spanning trees to their continuum analogues on the continuum random tree. Joint work with Eleanor Archer and Matan Shalev