# Scaling limits of loop-erased random walks and uniform spanning trees

@article{Schramm1999ScalingLO,
title={Scaling limits of loop-erased random walks and uniform spanning trees},
author={Oded Schramm},
journal={Israel Journal of Mathematics},
year={1999},
volume={118},
pages={221-288}
}
• O. Schramm
• Published 5 April 1999
• Mathematics
• Israel Journal of Mathematics
AbstractThe uniform spanning tree (UST) and the loop-erased random walk (LERW) are strongly related probabilistic processes. We consider the limits of these models on a fine grid in the plane, as the mesh goes to zero. Although the existence of scaling limits is still unproven, subsequential scaling limits can be defined in various ways, and do exist. We establish some basic a.s. properties of these subsequential scaling limits in the plane. It is proved that any LERW subsequential scaling…
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