Resumen de Conformal invariance of planar loop-erased random walks and uniform spanning trees

Gregory F. Lawler, Oded Schramm, Wendelin Werner

• This paper proves that the scaling limit of a loop-erased random walk in a simply connected domain Dsubsetneqq\C is equal to the radial SLE2 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 \pD is a C1-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⊂\pD, is the chordal SLE8 path in D¯¯¯¯ joining the endpoints of A. A by-product of this result is that SLE8 is almost surely generated by a continuous path. The results and proofs are not restricted to a particular choice of lattice.