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A spanning tree of a finite connected graph G is a connected subgraph of G that touches every vertex and contains no cycles. In this talk we will consider uniformly drawn spanning trees of ``high-dimensional’‘ graphs, and show that, under appropriate rescaling, they converge in distribution as metric-measure spaces to Aldous’ Brownian CRT. This extends an earlier result of Peres and Revelle (2004) who previously showed a form of finite-dimensional convergence. Based on joint works with Asaf Nachmias and Matan Shalev.
