Lawler, Gregory F.; Schramm, Oded; Werner, Wendelin Conformal invariance of planar loop-erased random walks and uniform spanning trees. (English) Zbl 1126.82011 Ann. Probab. 32, No. 1B, 939-995 (2004). Summary: This paper proves that the scaling limit of a loop-erased random walk in a simply connected domain \(D\subsetneqq\mathbb C\) is equal to the radial \(\text{SLE}_2\) path. In particular, the limit exists and is conformally invariant. It follows that the scaling limit of the uniform spanning tree in a Jordan domain exists and is conformally invariant. Assuming that \(\partial D\) is a \(C^1\)-simple closed curve, the same method is applied to show that the scaling limit of the uniform spanning tree Peano curve, where the tree is wired along a proper arc \(A\subset\partial D\), is the chordal \(\text{SLE}_8\) path in \(\overline D\) joining the endpoints of \(A\). A by-product of this result is that \(\text{SLE}_8\) is almost surely generated by a continuous path. 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