Conformal invariance of planar loop-erased random walks and uniform spanning trees
| dc.creator | Lawler, Gregory F. | |
| dc.creator | Schramm, Oded | |
| dc.creator | Werner, Wendelin | |
| dc.date | 2001-12-20 | |
| dc.date | 2003-03-10 | |
| dc.date.accessioned | 2026-07-07T10:22:29Z | |
| dc.date.available | 2026-07-07T10:22:29Z | |
| dc.description | We prove that the scaling limit of loop-erased random walk in a simply connected domain $D$ is equal to the radial SLE(2) path in $D$. 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 the boundary of the domain 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 $A$ on the boundary, is the chordal SLE(8) path in the closure of $D$ joining the endpoints of $A$. A by-product of this result is that SLE(8) is almost surely generated by a continuous path. The results and proofs are not restricted to a particular choice of lattice. | |
| dc.identifier | https://arxiv.org/abs/math/0112234 | |
| dc.identifier | http://arxiv.org/abs/math/0112234 | |
| dc.identifier | AnnalsProbab.32:939-995,2004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/175532 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | Complex Variables | |
| dc.subject | 60K35; 30C99; 60J99 | |
| dc.title | Conformal invariance of planar loop-erased random walks and uniform spanning trees | |
| dc.type | text |