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Diameter of uniform spanning trees on random weighted graphs
Luca Makowiec, Michele Salvi, Rongfeng Sun · 2023-11-03 · via math.PR updates on arXiv.org

For any edge weight distribution, we consider the uniform spanning tree (UST) on finite graphs with i.i.d. random edge weights. We show that, for bounded degree expander graphs and finite boxes of ${\mathbb Z}^d$, the diameter of the UST is of order $n^{1/2+o(1)}$ with high probability, where $n$ is the number of vertices.

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