... composition LR, it suffices to prove(2.2) for LR with γ in place of α. Independence of the relations L and R,together with (2.2) for L and for R with β in place of α implyP[xLRz, yLRw] ≤a,b∈ZdP[xLa, ... from Wilson [15] for picking uniformly a spanning tree in a finite graph. Let {v1,v2, } be anGEOMETRY OF THE UNIFORM SPANNING FOREST477arbitrary ordering of the vertices of a transient graph ... OF THE UNIFORM SPANNING FOREST485The lemma follows by consideration of the uniform spanning forest onZdas a weak limit of uniform spanning trees in finite subgraphs (with wiredcomplements),...