We show that the local limit of the uniform spanning tree on any finite, simple, connected, regular graph sequence with degree tending to \(\infty \) is the Poisson(1) branching process conditioned to survive forever. An extension to “almost” regular graphs and a quenched version are also given.

中文翻译：

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均匀生成树的局部极限

我们表明，均匀生成树在任何有限的、简单的、连通的、规则的图序列上的局部极限，其度数趋向于\(\infty \)是 Poisson(1) 分支过程，条件是永远存在。还给出了“几乎”正则图的扩展和淬火版本。