PR ] 2 0 D ec 2 00 1 Conformal invariance of planar loop-erased random walks and uniform spanning trees

@inproceedings{Lawler2001PR2,
title={PR ] 2 0 D ec 2 00 1 Conformal invariance of planar loop-erased random walks and uniform spanning trees},
author={Gregory F. Lawler and O. Schramm and Wendelin Werner},
year={2001}
}

This paper proves that the scaling limit of loop-erased random walk in a simply connected domain D $ 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 ∂D 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… CONTINUE READING