Wired Uniform Spanning Forest

The wired uniform spanning forest on an infinite connected locally finite graph is the weak limit of uniform spanning trees on finite exhaustions with the exterior identified to a single boundary vertex. Retain the tree edges internal to each finite region when taking the limit. The law may differ from the free uniform spanning forest, which leaves boundary vertices distinct. The choice of boundary convention is therefore part of the definition, even though both limits are probability laws on spanning forests of the same infinite graph.